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A  STUDY  OF  TI3E  FUNDAMENTAL  PRINCIPLES  OF  CURRENT  METERS 


A  study  of  the  fundamental  principles  of  current  meters 


By 

Joseph  Ridgeway  Gunn,  Jr. 
B.S.  (University  of  Texas)  1921 

THESIS 
Submitted  in  partial  satisfaction  of  the  requirements  for  the  degree  of 

MASTER  OF  SCIENCE 
in 

Mechanics 

in  the 
GRADUATE  DIVISION 

of  the 
UNIVERSITY  OF  CALIFORNIA 


Approved 


Instructor  in  Charge 


Deposited   in  the  University  Library          /t+    f^  /ff  12- 


Date  Librarian 


PREFACE. 


The  steady  development  of  water  resources  for  hydraulic 
power  and  irrigation  purposes,  and  a  consequently  increasing  de- 
mand for  current  measuring  instruments  more  accurate  than  any 
which  have  heretofore  been  designed  has  suggested  that  an  inves- 
tigation be  made  of  the  defects  existing  in  the  present  meters. 
A  study  of  the  problem  reveals  an  interesting  fact,  i.  e.,  that 
all  basic  principles  seem  to  have  been  given  insufficient  con- 
sideration by  the  designer.  The  effects  of  eddy  currents  ap- 
parently have  never  been  considered;  stream  lines  have  always  as- 
sumed parallel;  the.  requirements  for  the  very  low  velocities  en- 
countered in  irrigation  investigations  have  been  ignored. 

Although  the  courts  of  this  country  recognize  no  stan- 
dard, they  usually  accept  the  gagings  determined  by  a  turbine  type 
meter  because  of  its  popularity. 

The  absence  of  literature  on  the  subject  of  fundamentals 
themselves  makes  the  acutenes?  of  the  situation  more  easily  realized. 
The  results  of  extensive  investigations  of  the  principles,  in  so 
far  as  the  writer  has  been  able  to  determine,  have  never  been 
recorded  by  American  engineers.  Schmidt,  Sandstrom,  Bateau  and 
Spper  have  investigated  many  phases  of  the  problem;  but  the  Euro- 
pean requirements  are  essentially  different  from  the  American. 

3ver,  very  little  of  these  authors'  works  were  available,  but 
those  few  articles  which  could  be  obtained  were  invaluable  to  the 
writer. 

The  preparation  of  this  thesis  is  a  step  into  a  new  field, 
and  like  all  things  new  it  will  likely  receive  a  great  deal  of 
criticism  all  of  which  the  writer  welcomes. 

Besides  an  investigation  of  some  of  the  fundamentals  of 
stream  flow,  a  theory  of  resistance  or  interference  as  advanced  by 
fir.  E.  J.  Hoff  has  been  set  forth.  Mr.  Hoff  has  been  connected 
with  the  Department  of  Agriculture,  Bureau  of  Public  Ro»d-s,  Di- 
vision of  Rural  Engineering,  Irrigation  Investigations,  for  over 
16  years  during  which  time  he  has  been  intensely  interested  in  the 
current  meter  problem  and  has  contributed  much  to  its  advancement. 

An  absence  of  comparative  tests  between  the  turbine  type 
of  meter  and  the  propeller  type  of  meter  will  be  particularly  con- 
spicuous in  this  paper.  The  writer  first  thought  of  making  tests 


in  the  weir  channel  here  in  the  hydraulic  labratory  of  the  Univer- 
sity of  California,  but  after  more  thought  on  the  subject  the  idea 
was  abandoned  because  the  results  obtained  in  a  single  channel  would 
be  of  little  value  4  A  series  of  tests  of  this  kind,  to  be  of  any 
worth,  would  require  a  long  period  of  time,  and  should  be  conducted 
under  government  supervision.  Tests  should  be  made  in  channel?  of 
different  cross  sectional  areas  and  proportions,  with  varying 
velocities  and  depths  of  water,  and  it  would  be  highly  desirable 
to  determine  a  factor  which  would  show  a  definite  relation  between 
the  type  and  the  factors  listed.  The  huge  volume  of  data  thus  ob- 
tained would  then  warrant  a  critical  comparison  of  types. 

The  writer  is  deeply  indebted  to  the  Berkeley  office 
of  the  Department  of  Agriculture,  and  especially  to  Mr.  Hoff, 
for  its  encouragement  in  the  preparation  of  this  paper.  Thanks 
are  also  due  the  Spring  Valley  ~7ater  Company,  San  Francisco, 
for  the  use  of  their  Belmont  rating  station. 


J.  R.  G. 


Berkeley,  California, 
April,   1922. 


CONTENTS.  .   . 

Page 
Preface iii 

I.  INTRODUCTION. 

1.  Brief  History  of  Current  Meter  Development..    1 

2.  Principle  of  Meter  Method  of  Measuring 

Stream  Flow  Is  Wrong 3 

3.  Purpose  of  Thesis 4 

4.  Only  Scientifically  Designed  Meter:  Ott 4 

5.  More  Figid  Demands  Placed  Upon  Meter  When 

Used  for  Irrigation  Work 6 

II.  FUNDAMENTAL  PRINCIPLES  OF  CURRENT  METERS. 

A.  Fluid  Motion  and  Obstacles. 

6.  Obstacles 6 

7 .  Eddy  Effects 9 

8.  Example  of  Rod  in  Stream 13 

B.  Hoff  Theory  of  Resistance. 

9.  Explanation 17 

10.  Vertical  Shaft  Meters 17 

11.  Explanation  of  Turbine  Rotation 24 

12.  Other  Characteristic  Curves  for  Vertical 

Shaft  Instruments 27 

13 .  Horizontal  Shaft  Instruments 31 

14 .  Summary 40 

C.  Supplementary  Tests. 

15.  Purpose 42 

16.  Effects  of  '.Vires,  Rods,  Yokes  and  Cables  on 
Current  Meter  Operation 42 

17.  Tests  of  Price  Meters  as  Horizontal  Shaft 
Meters 50 

III.  REQUIREMENTS  FOR  IDEAL  CURRENT  METER  MEASUREMENTS. 

16.  Requirements 52 

19.  possibility  of  Realizing  Ideal  Requirements.   53 

IV.  THE  VERTICAL  SHAFT  TURBINE  1ETER  VS.  THE  HORIZONTAL 
SHAFT  PROPELLER  METER. 

20.  Advantages  of  the  Vertical  Shaft  Turbine 

Type  Meter 58 

21.  Disadvantages  cf  the  Vertical  Shaft  Turbine 

Type  Meter 59 

22.  Advantages   of  the  Hoff  Horizontal  Shaft 
Propeller  Type  lleter 61 

23.  Equation  for  the  Rotation  at  Various  Values 

of  the  Angle  $ 71 

24.  Disadvantages  of  the  Hoff  Horizontal  Shaft 
Propeller  Type  Meter 82 

V.  CONCLUSIONS. 

25.  Conclusions 

Bibliography 85 

Index 87 


A  STUDY    OF    THE  FUNDAMJTrTU,  PRINCIPLES   OF  CURRENT  METERS 


I.      INTRODUCTION. 


1.     Brief  History  of  Current  Meter  Development  .  —  Instru- 
ments   of  various   forms   for   the  measurement   of  stream  flow  have  been 
in  general  use   for   one   hundred  and   fifty  years   or  more.     The   first 
instruments   employed  were   simple  wooden  or  cork  floats;    later  these 
were   replaced  by  semi-floating  rods    of  different  types.     These   rods 
were   of  wood,    cork,    or  metal  tubing  weighted  at  the  bottom  so  as  to 
float  vertically.     As   the   science    of  hydrology  developed,   and  eco- 
nomic conditions  demanded  the   conservation  and  industrial  utiliza- 
tion of  hydraulic  power,  more  accurate   instruments  were    in  demand. 

One   of  the   first  meters   of  modern  design  was   invented  by 
Revy  after   considerable   experience   in  gaging  South  American  rivers. 
No  thought  "was   given  the   fundamentals   in  the   design  of  this    instru- 
ment;   since   the   propeller     rotated  in  a  moving  stream,    no  farther 
study  of  the   theory  seemed  necessary.     This  meter  was  equipped  with 
a  6   in.   propeller   of  the  Griffith  screw  type  as  used   on  ships.     The 
blades  were  mounted  around  a  hollow  metal  boss,  the   idea  being  to 
minimize   instrumental  friction  by  reducing  the   relative  weight   of 
the    rotating  parts.     All   of  the   early  meters,   like   the   Revy  meter, 
were   of   the  horizontal   shaft  type,  very  bulky  in  design,   and     bur- 


^•In  this   paper,   a  distinction  will  be  made  between  "turbine"   and 
propeller".     A  turbine  may  be  defined  as  a  number  of  cups  mounted 
concentrically  upon  a  vertical   shaft.     A  propeller  may  be  defined 
as   a  number   of  blades  mounted  radially  upon  a  horizontal   shaft. 

(1) 


(1)  Price  Meter,  Model  623,  as  cable  meter.  Meter  equipped  with  Hoff 
improved  1:1  and  5:1  contact  chamber,  and  turbine  spindle. 

(2)  Price  Meter,  Model  618,  with  eccentric  base. 

(3)  Price  Meter,  Model  618,  with  concentric  base. 

Fig.  1. 


dened  with  a  mass   of  non-revolving   parts.     These   instruments,    in 
spite   of  floating  bosses   and  other   similar  devices,    showed  a  very 
large   friction  factor.     This  general    type    of  instrument   in  a  very 
materially  improved   form  is   on  the  market  today  under  the   names   of 
Haskell,  and  Ott. 

In  1885,  W.   G.   Price,  Assistant  Engineer  of  the   Corps   of 
Engineers,   United  States  Army,  was  engaged   in  measuring  the   flow  of 
the   Ohio  River.     At  this    particular  time  the  river  was   at  a  very 
high  stage,   and  quite  muddy.     Mr.   Price  experienced  a  great  deal  of 
difficulty  with  the  horizontal  shaft  type   of  meter,   and  he   designed 
the    original  Price  meter  which   is    nothing  more   nor  less  that   a  modi- 
fied type   of  anemometer.     As   far  as   it  was   possible  to  estimate,   this 
new  meter  gave  fair  results. 

As   can  be    seen  from  this   very  brief  sketch  of  the   history 
of  current  meters   given  above,   the   instruments   have   never  been  de- 
signed  from  a  basis    of  fundamentals.     The   designer  seems  to  have 
always  been  satisfied  with  the   fact  that   his  meter  rotated   in  the 
stream,   and  has   gone   no  further. 

2.     Meter  Method   of  Measuring  Stream  Flow. — In  the   first 
place,    the  meter  method   of  measuring   stream   flow  will  never  pro- 
duce accurate  results.     As  will  be   shown  later,   if  any  body,  no 
matter  how  saall,   be   immersed   in  water,    it  will   set  up  eddy 


The   use   of  this  word   is   likely  to  confuse  the   reader.     To  avoid 
this,   the  writer  will  give   his  definition:     An  eddy  current   is   a 
current  which  has   suffered  a  perceptible   change   of  direction.      The 
term  is   usually  applied  to  a  current  whose  direction  has  been  com- 
pletely reversed.     Eddy  forces   refer  to  the   new  forces   exerted  by 
the   eddy  currents . 


< 
' 

"  <. 

, 
• 

I  O- 

. 

(. 

7      .Pi- 

: 


. 


f drees  and  cross  currents.  This  alteration  of  the  original  forces, 
and  direction  of  stream  filaments  introduces  an  error  from  the  very 
beginning.  A  perfect  meter  is  then  out  of  the  question. 

5.  Purpose  of  Thesis.— It  is  the  purpose  of  this  thesis, 
therefore,  to  point  out  certain  fundamental  principles  of  current 
meter  design,  and  to  show  that  a  careful  study  of  the  existing  evils, 
and  a  combination  of  the  lesser  evils,  modified  as  far  as  possible, 
will  result  in  a  meter  whose  observations  will  show  greater  precision. 

4.   Only  Scientifically  Designed  Meter:  Ott.— The  only 
scientifically  designed  meter  with  which  the  writer  is  familiar  is 
the  Ott  meter  manufactured  by  A.  Ott,  Kempten,  Bavaria.  The  blades 
of  the  propeller  were  designed  after  a  mathematical  development, 
and  should  theoretically  offer  no  interference  to  parallel  stream 
filaments.  Under  actual  conditions,  however,  the  instrument  offers 
a  small  interference,  though  it  is  ce'rtainly  a  minimum.   In  low 
velocities,  the  Ott  meter  shows  a  somewhat  high  friction  factor, 
which  is  not  to  be  desired,  but  for  the  higher  velocities,  taking 
all  factors  into  consideration,  it  is  one  of  the  best  instruments 

to  be  had. 

The  meter  was  designed  upon  the  assumption  that  all  stream 
filaments  were  parallel.   If  this  were  the  case,  this  instrument  to- 
gether with  many  other  types  of  meter  manufactured  today  would  be 
very  nearly  perfect;  but  this  is  not  the  case,  for,  as  will  be  shown 
later,  parallel  filaments  exist  only  in  theory. 

Since  parallel  currents  do  not  exist,  would  it  not  be  bet- 
ter in  the 'design  of  current  meters  to  choose  between  evils,  and  se- 


, 


. 
. 

«U  ^IJ 


, 


(1)  Hoff  Meter,  Model  21,  as  rod  meter. 

(2)  Hoff  Meter,  Experimental  Model,  as  cable  meter. 

(3)  Hoff  Meter,  Model  22,  as  rod  meter. 

Fig.  2. 


lect  the   lesser   ones?      In  other  words,    if  a  meter  could  be  designed 
which  would  automatically  utilize   only  those   components   of  stream 
velocity  perpendicular  to  the  base  plane   of  measurement,  even 
though  this   instrument  offered   somewhat  more   interference  to  stream 
flow,  would   it  not  be  the  better  plan  to  design  the  meter  after  the 
former  principle? 

5.  More  Rigid  Demands   Placed  upon  Meter  when  Used   for 
Irrigation  Work.— As   it  becomes   necessary  to  cultivate   lands   located 
in  sections  which  receive    only  seasonal   rainfall,    irrigation  is   com- 
ing more   into  practice.     This   phase   of  hydraulic  engineering  has 
placed  more  exacting  demands  upon  the   current  meter.      In  the   first 
place,   the   low  velocities   usually  encountered   in  irrigation  canals—- 
the  average   of  which  is   below  2   ft.   per  second — demand   a  meter  which 
will  accurately  indicate  these  velocities.     This   obviously  necessi- 
tates the  reduction  of  the  friction  factor.     In  the   second  place, 
the  very  small   cross   section  of  the    irrigation  canal  requires  a 
meter  whose   propeller  or  turbine   is   of  a  smaller  diameter  than  that 
of  any  meter  being  manufactured  today.     The  Hoff  meter,  with  which 
this    paper  will  deal   at   considerable   length,  was   designed  primarily 
to  meet  the   new  and  more   rigid   requirements,   though  the   latest   style 
meter,  model   22,  will   function  equally  well   in  the  higher  velocities. 

II.      FUNDAMENTAL  PRINCIPLES   OF   CURRENT  METERS. 
A.     Fluid  Motion  and   Obstacles. 

6.  Obstacles .--If  any  object  is   immersed   in  a  moving 
stream  of  perfect  fluid,  which  fluid  may  be  defined  as   one  without 
viscosity,   each  filament  will  flow  around  that    object   in  perfectly 


•". 


. 
-- 

.89. 

t 

, 


smooth  stream  lines,  and  at  every  point  will  be  tangent  to  the  sur- 
face of  the  object.   No  fluid,  however,  is  entirely  devoid  of  vis- 
cosity, and  the  existence  of  this  characteristic  causes  the  flow  to 
be  sinuous  or  eddying.  Thus,  if  some  object  be  immersed  in  water, 
the  stream  lines  will  not  be  smooth.   No  matter  how  small  or  large 
the  object,  whether  it  be  a  pebble  or  a  huge  boulder,  eddying  effects 
and  cross  currents  will  be  produced  to  a  greater  or  lesser  degree, 
and  the  resulting  stream  lines  present  a  problem  infinitely  more 
difficult.  IVith  the  exception  of  the  simplest  cases  which  Prof.  Hele 
Shaw  has  worked  out  very  successfully,  the  problem  of  stream  line 
flow  absolutely  defies  mathematical  analysis.   It  is  necessary,  there- 
fore, to  make  all  the  experiments  possible,  and  draw  such  conclusions 
as  seem  reasonable. 

Since  any  object,  regardless  of  its  size,  will  produce  eddy 
currents  and  cross  currents,  it  is  obviously  impossible  for  parallel 
filaments  to  exist  under  actual  field  conditions;  yet  it  is  under 
this  assumption  that  practically  all  current  meters  have  been  de- 
signed. Aside  from  foreign  obstacles  themselves,  the  viscosity  of 
the  water  serves  to  produce  non-parallel  filaments.  Velocity  con- 
tours and  vertical  velocity  curves  both  substantiate  this  statement. 
From  these  curves,  it  is  seen  that  the  velocity  varies  from  a  mini- 
mum at  the  bed  to  a  maximum  somewhere  near  the  surface,  the  curve 
being  theoretically  a  parabola.  Contour  curves        show  similar 
results:  i.  e.,  the  velocity  varies  from  a  minimum  at  the  sides  and 
bottom  of  the  channel  to  a  maximum  at  a  point  near  the  center  of  the 
surface.  Since  the  velocity  of  a  stream  varies  throughout  the  cross 
section,  the  viscous  dragging  effect  existing  between  filaments  al- 


ev-n.  , 

rfflXH    W< 


u> 


ters  the  direction  of  the  filanents  in  a  very  uncertain  way.   Or, 
to  put  it  in  the  words  of  another,  "resistance  is  not  caused  by  the 
liquid  rubbing  against  their  beds:  it  is  almost  entirely  caused  by 
the  liquid  changing  shape,  and  so  forming  'eddies1.11' 

7.  Eddy  Effects. --Consider  the  rectangular  plate,  AB,  im- 
mersed in  a  moving  stream  as  shown  in  Fig.  3  (a).  The  water  adheres 
to  the  surface  of  the  plate,  and  consequently  this  film  is  not  in 
motion.  The  stream  filament  which  just  misses  the  edge  of  the  plate 
would  be  expected  to  follow  the  course  AC1  on  account  of  its  inertia, 
"its  proximity  to  the  body  and  the  reduction  in  motion  caused  by  the 
retardation  of  the  layers  of  the  fluid  in  its  immediate  neighborhood, 

however,  cause  the  particles  to  tend  to  move  along  a  path  of  smaller 

2 

radius  of  curvature  and  the  stream  line  bends  inward  along  AC."  '  In 

the  same  way,  each  neighboring  filament  is  affected.  Consequently, 
behind  the  plate  two  whirls  or  eddies  will  be  observed,  one  at  each 
edge.  These  eddies  are  produced  periodically,  and  finally  at  some 
distance  behind  the  plate  they  merge  with  the  other  filaments. 

Often  times  another  type  of  eddy  is  formed  as  shown  in 
Fig.  3  (b).  This  is  different  from  the  first  only  in  the  time  at 
which  the  whirls  appear,  the  whirls  at  one  edge  seeming  to  lag  be- 
hind those  at  the  other  edge.  Many  experiments  have  been  conducted 
for  the  purpose  of  ascertaining  just  when  to  expect  the  second  type 
of  eddy,  but  no  definite  conclusions  have  as  yet  been  drawn.  How- 
ever, it  seems  reasonable  to  assume  that  the  latter  type  would 


"Motion  of  Liquids",  by  R.  de  Villamil. 
2"Aeronautics  in  Theory  and  Experiment",  by  Cowley  and  Levy. 


' 


. 


eecf  oVBri   a. 


only  be  produced  when  some  non-symmetrical  disturbance  had  entered. 

It  is  not  possible  to  determine  the  magnitude  of  these 
eddy  forces,  nor  can  it  be  said  in  just  what  manner  they  resolve 
themselves.  However,  their  effect  is  felt  in  the  force  required  to 
hold  the  plate  in  the  stream,  and  their  importance  cannot  be  over- 
estimated, because,  as  will  be  shown  later,  the  rotation  of  the 
Price  meter  turbine  depends  largely  upon  their  existence. 

Upon  approaching  the  plate,  the  stream  filaments  are 
slowed  down;  but  in  passing  around  the  edges  and  moving  into  the 
whirls,  they  are  again  accelerated.  n.   .   .  the  total  energy 
per  unit  volume  at  a  given  point  in  a  stream  filament  is  composed 
of  potential  energy,  or  pressure,  and  kinetic  energy,  which  is 
measured  by  the  velocity:  and  the  sum  of  these  two  is  a  constant 
at  all  points  of  the  stream  filament.  Expressed  generally,  per 

unit  volume  of  the  stream  filament, 

p 

p   +  gmv     a  constant 

potential  energy  •••  kinetic  energy  =  constant 
where   p   =  pressure,   v   *  velocity,   and  m  =  the  density  of  the   liquid; 

p 

and  this   p   +  igmv     must   retain  the   same  value   at   all   points   of  the 
same   stream  line — provided,   of  course,   that   it  always   lies   in  the 
same  horizontal  plane.      .      .      .     Potential  energy  may  be  converted 
into  kinetic  energy,    or  vice  versa,   but  the   sum  of  the  two  must  re- 
main constant."1     Consequently,   as   the  velocity  of  these   filaments 


1"Motion  of  Liquids",   by  R.   de  Villamil. 


11 


increases,  the  kinetic  energy  increases,  while  the  potential  energy 
decreases  by  an  equal  amount,  because  the  sum  of  the  kinetic  and 
potential  energy  must  at  all  times  be  a  constant.   In  other  words, 
the  whirls  or  vortices  are  characterized  by  a  pressure  which  is 
lower  than  that  of  the  neighboring  fluid,  but  the  eddies  thus 
formed  exert  a  very  appreciable  "reactive"  force,  or  force  oppo- 
site in  direction  to  that  of  the  original  velocity  force. 

The  pressure  on  the  plate  is  made  up  of  two  components: 
one  is  the  "velocity  pressure",  and  the  other  is  the  "static  pres- 
sure".  If  the  liquid  were  stationary,  the  static  pressures  on 
each  side  of  the  plate  would  balance  themselves,  and  in  the  ab- 
sence of  any  velocity  pressures,  no  force  would  be  required  to  hold 
the  plate  up;  but  as  soon  as  the  stream  begins  to  move,  an  entirely 
different  condition  has  to  be  contended  with.  The  static  pressure 
on  the  anterior  face  is  increased  very  slightly  due  to  a  piling  up 
of  the  water.  The  static  pressure  on  the  posterior  face  is  consider- 
ably reduced,  as  explained  above,  and  partly  on  account  of  this  re- 
duction, eddy  currents  are  formed  which  exert  a  velocity  pressure 
on  the  posterior  face  opposite  in  direction  to  the  velocity  pres- 
sure exerted  on  the  anterior  face. 

Thus,  it  has  been  shown  again  that  due  to  eddy  currents 
set  up  in  the  rear  of  the  plate  the  force  required  to  hold  the 
plate  in  position  against  the  velocity  pressure  of  the  oncoming 
stream  is  somewhat  smaller  than  the  force  of  the  velocity  itself. 


12 


Fig.  4. 


8.  Example  of  Rod  in  Stream.  — If  a  rod  is  immersed  in  a 
moving  stream,  a  side  elevation  of  the  above  phenomena  may  be  ob- 
served.  Fig.  4  sho-ws  a  rod  meter  held  in  a  stream,  with  the  direc- 
tion of  the  stream  filaments  diagrammatically  represented.  At  a 
distance  _c  in  front  of  the  rod,  the  stream  filaments  begin  to  slow 
down  and  pile  up,  and  immediately  in  front  of  the  rod  the  water  is 
raised  a  distance  a  above  the  normal  level  of  the  stream.  At  this 
point  in  the  hump,  the  filaments  momentarily  come  to  rest  on  account 
of  a  transposition  of  pressures:  i.  e.,  due  to  the  presence  of  the 
rod  as  an  obstacle,  the  velocity  pressure  or  energy  is  all  consumed 
in  lifting  the  water  to  the  height  a.   In  other  words,  the  velocity 
pressure  is  reduced  to  zero  while  the  static  pressure  is  increased 
to  a  maximum.  Between  the  up-stream  and  down-stream  sides  of  the 
rod  there  is  an  immediate  and  quite  pronounced  drop  in  the  water 
level,  as  shown.  Behind  the  rod  there  is  a  concave  surface  or  hol- 
low into  which  the  water  rushes  from  its  slightly  higher  elevation 
in  front.  The  depth  of  the  hollow  reaches  a  maximum  value  indicated 
by  b,  and  at  a  distance  d  behind  the  rod  the  filaments  reach  the  nor- 
mal level  of  the  stream  where  the  disturbance  is  finally  absorbed 
by  the  more  smoothly  moving  filaments .  The  formation  of  whirls  or 
vortices  explains  the  presence  of  this  hollow.   In  the  same  way 
that  eddy  currents  were  formed  behind  the  plate,  as  described  in 
Section  7,  they  are  formed  behind  the  rod  in  this  case,  and  as  part 
of  the  static  pressure  is  changed  into  velocity  pressure  in  the 
vicinity  of  the  eddies,  the  pressure  in  the  rear  of  the  rod  is  re- 
duced, with  the  consequent  formation  of  a  slightly  vacuous  space 
or  hollow. 


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14 


If  the  stream  is  moving  slowly,  the  slowing  down  of  the 
filaments  can  be  detected  at  e.  considerable  distance  in  front  of  the 
rod,  but  the  water  is  lifted  to  only  a  very  slight  elevation.  In  the 
same  way,  b_  is  small,  and  d_  is  large.  Vice  versa,  if  the  stream  is 
moving  rapidly,  _c  and  d_  are  small,  but  ia  and  £  are  proportionately 
larger.   In  other  words, 

c  =  k  X  1 
V 

a  =  k2  X  V 

b  =  k_  X  V 
o 

c  =  k  X  1 
4   V 

where,  Ic  ,  k  ,  k_  and  1^  are  constants,  and  V  is  the  velocity  of  the 
stream. 

'.Then  an  obstacle  is  placed  in  a  moving  stream,  the  filaments 
split  in  front  of  the  obstacle  on  what  might  be  termed  a  "liquid 
prow",  and  proceed  around  the  edge  as  shown  in  Fig.  3.  This  same 
phenomena  is  present  in  the  case  of  the  rod  in  the  stream.  The  edfe 
of  the  liquid  prow  is  at  a  distance  c1  (not  shown)  •  c  in  front  of 
the  rod.  The  stream  divides  at  this  point,  flows  around  the  sides 
of  the  rod,  and  finally  merges  with  the  smoothly  flowing  filaments 
at  a  distance  d'  (not  shown)  =  d  behind  the  rod.   If  the  stream  is 
moving  slowly,  c1  and  d1,  and  the  distance  out  from  the  sides  of 
the  rod  to  which  the  disturbance  can  be  felt  are  relatively  large. 
Vice  versa,  if  the  stream  is  moving  rapidly,  these  distances  are 
much  shorter.   The  stream  filaments  directly  in  front  of  the  rod, 


a,  b,  c  and  d  are  not  drawn  to  scale. 


15 


after  having  suffered  a  change  in  internal  energy- -having  gained  an 
amount  of  potential  energy  at  the  expense  of  the  kinetic  energy- 
proceed  around  the  front  of  the  rod  at  a  lower  velocity  than  that 
of  the  unaltered  filaments.  As  soon  as  they  reach  the  edge  of  the 
rod,  their  direction  is  changed,  and  in  moving  into  the  vacuous 
space  behind  the  rod  they  give  up  part  of  their  potential  energy 
which  is  changed  immediately  into  kinetic  energy,  and  due  to  the 
viscosity  this  increased  velocity  forms  very  rapidly  moving  whirls 
or  eddies. 

However,  the  point  to  be  emphasized  is  that  the  stream 
filaments  directly  in  front  of  the  rod  turn  from  their  original 
course  with  about  the  same  amount  of  velocity  energy  in  all  cases, 
independent  of  the  original  velocity;  but  the  greater  the  original 
velocity,  the  higher  the  distance  a  to  which  the  water  is  piled. 
In  other  words,  all  "surplus"  velocity  energy  is  transformed  into 
potential  energy  in  the  piling  up  process,  and  the  filaments  depart 
from  their  original  course  with  a  constant  velocity  energy.  The 
greater  the  velocity  the  more  difficult  it  is  for  the  filaments 
whose  pressures  have  been  rearranged  to  push  aside  the  undisturbed 
filaments,  and,  in  general,  it  may  be  stated  that  the  area  of  the 
surface  of  the  stream  in  which  the  disturbance  is  felt  is  inversely 
proportional  to  the  velocity  of  the  stream. 

It  is  this  rod  phenomena  which  explains  the  surface 
curve  of  a  current  meter. 


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17 


B.  Hoff  Theory  of  Rosistance . 

9.  Explanation. — The  Hoff  theory  of  resistance,  or  theory 
of  interference  as  it  might  well  be  called,  deals  with  rating  curves 
for  the  various  types  of  current  meters  from  a  standpoint  of  the  in- 
terference offered  oncoming  stream  filaments  by  the  rotating  member 
itself.   It  explains  the  irregularities  ordinarily  found  in  rating 
curves,  and  establishes  a  definite  relation  or  connecting  link  between 
the  test  curve  and  the  theoretical  or  ideal  curve.   Incidentally  the 
theory  offers  an  explanation  for  the  rotation  of  a  turbine;  and  it 
might  be  said  here  that  in  none  of  the  scant  amount  of  literature 

on  the  subject  of  current  meters  which  the  writer  has  been  able  to 
obtain  has  he  seen  any  explanation  of  this  action  put  forth. 

10.  Vertica^l  Shaft  Meters. — Fig.  5  shows  the  normal 
characteristic  rating  curve  of  a  vertical  shaft  meter,  such  as  the 

Gurley  (or  Price),  Lietz,  and  Lallie.  The  "starting  velocity  curve" 

2 

begins  at  0.05  ft.  per  second — zero  revolutions  per  second — and 


Figs.  5,  9,  10,  11,  12  and  15  are  general  curves,  not  applicable 
to  any  one  particular  meter,  but  simply  cEar&cteristic  of  the 
type  as  a  whole.  They  have  been  reproduced  from  L'r.  Hoff's  "Cur- 
rent Keter  Studies".  Certain  sharp  breaks  will  be  observed  in  these 
curves.   These  are  exaggerated  in  order  that  the  irregularity  at 
the  particular  point  will  be  plainly  evident.   In  all  of  the  rating 
curves  included  in  this  paper,  the  heavy  line  indicates  the  test 
curve,  while  the  light  line  indicates  the  theoretical  curve  which 
passes  through  the  origin. 

Although  the  starting  velocity  curve  begins  at  0.05  ft.  per  second, 
the  meter  will  not  rotate  until  about  0.16  ft.  per  second.  Veloci- 
ties above  0.5  ft.  per  second  are  considered  reliable  by  Messrs.  TIT. 
&  L.  E.  Gurley  in  their  "Manual  of  Gurley  Hydraulic  Engineering  In- 
struments". Velocities  as  low  as  0.2  ft.  per  second  are  not  un- 
common in  the  rice  fields. 


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19 


Table  1. 

Rating  of  Price  Meter,  Model  142.  June  21,  191S. 

Time  in  Revo-     Revolutions  Ft.  per 
seconds,   lutions.   per  second,   second. 

Course:  120  ft. 

16.5  53  3.21  7.28 

18  52  2.89  6.667 

20.75  52.5  2.534  5.783 

21  52  2.476  5.714 

26  52  2  4.615 

26.5  52  1.962  4.528 

33.61  52  1.562  3.603 

36.5  52  1.425  3.288 

38.5  52  1.35  3.117 

48  52  1.083  2.5 

62  51+  2.25  1.935 

75  51+  .69  1.6 

Course:  60  ft. 

45  25+  .55  1.333 

50.5  25+  .5  1.188 

91  23.75  .261  .659 

76  24  .317  .789 
115  23  .2  .522 
138  22.5  .164  .435 
151.5  22  .145  .396 
188.5  21  .111  .316 


ends  at  2.2  ft.  per  second — 1  revolution  per  second.  Above  the  veloci- 
ty of  2.2  ft.  per  second  lies  the  "higher  velocity  curve"  which  coin- 
cides with  the  ideal  curve  through  the  origin. 

An  explanation  of  these  new  terms  would  not  be  out  of  place 
at  this  time.  The  ideal  curve  for  a  vertical  shaft  instrument  is  a 
straight  line  drawn  through  the  origin  and  as  many  observed  points 
as  possible.  The  term  "starting  velocity  curvo"  is  used  to  designate 
the  lower  section  of  the  rating  curve, whic h  is  a  curve,  but  which, 
for  practical  purposes,  is  usually  approximated  with  a  straight  line. 
The  upper  section  of  the  curve  which  is  a  straight  line  will  be 
known  as  the  "higher  velocity  curve".  Field  observations  are  only 
reliable  when  they  are  above  the  starting  velocity. 

What  causes  the  break  in  this  rating  curve?  Heretofore, 
it  has  been  generally  accepted  that  instrumental  friction  was  en- 
tirely responsible  for  this  irregularity,  but  this  is  not  the  case. 
Although  instrumental  friction  does  exist,  it  is  almost  negligible. 
The  important  factor,  however,  is  the  interference  of  the  turbine 
with  the  oncoming  stream  filaments. 

Fig.  6  shows  an  actual  rating  curve  of  a  Price  meter. 
However,  the  curve  is  not  different  from  the  characteristic  curve 
just  described,  so  no  discussion  is  necessary. 

Figs.  7  and  8  represent  stream  filaments  flowing  past  a 
Price  meter  turbine.  Fig.  7  is  a  characteristic  picture  of  the 
filaments  when  their  velocity  is  below  2.2  ft.  per  second.  A 
close  observation  of  the  stream  lines  and  their  relation  to  the 


Fig.   7. 

turbine   is   invitad.     Consider  the   lines  approaching  the  tur- 
bine  as  being  parallel.     Upon  meeting  the  turbine  their 
course   is   altered  to  accommodate  the   rotating  obstacle.     From 
zero  to  1  revolution  per  second,   or  from  zero  to  6  cups  per 
second,  the  water  has  time  to  enter  the  space  within  the   cups, 

and  it   is  this    interference   of  the   filaments  with  the   rotation, 
plus  a  small  friction  factor,  that  causes  the   starting  veloci- 


22 


Fig.   8. 

ty  section  of  the  rating  curve  to  lie  below  the   ideal  curve. 
10   of  the  filaments   flow  around  the   outside   of  the  turbine 
while   others  flow  in  between  the   cups  producing  certain  eddy 
currents  and  whirls. 

Now  observe  the  filaments  as  pictures  in  Fig.   8. 
Here,   their  velocity  is   2.2  ft.   per  second,   or  more.     What 
is  the  difference  between  the  filaments   in  thi  s  picture  and 
Ihose   in  Fig.   7?     First,  none   of  the  filaments  are   able  to 


23 


flow  in  between  the   cups,   because   at   this  velocity  the  turbine 
is   moving  with  a  velocity  of  1   revolution  per  second,  which 
is   equivalent  to  6  cups   per   second,    and  this    is    sufficient 
to  shut   out  the   oncoming  filaments.      Second,   an  eccentric, 
solid,  whirling  mass   is    observed  within   the   central   space. 
Third,  the   lines   approaching  and  departing  from  the   tur- 
bine  appear  to  be  more   radically  disturbed  at  this  higher 
rotation. 

It   is   this    factor  which  accounts   for  the  break   in 
the   rating   curve.      From  this   point  up,   the  meter   is    rotating 
so  rapidly  that  the   filaments   cannot  enter  the   region  between 
the   cups.      In  fact  the    obstacle  presented  to  the  moving  fila- 
ments  is   now  entirely  different   from  that   for  the   lower  ve- 
locities.     It   is   a  solid  mass,   the   center  being  filled  with 
water  which  rotates   at  the   speed  of  the  turbine.     A  side 
elevation  of  the   turbine   at   this   time  would  be   a  mass  with 
parallel  top  and  bottom  and   rounded  ends.      So,   the   rota- 
tion above   2.2  ft.   per   second  may  be   considered  as   normal, 
because   at  this   point  the   interference   factor  is   a  minimum, 
and   as  the   shape   of  the   obstacle   remains  unchanged  at  the 
higher  velocities,    it    is   constant;   and  with  a  constant   and 
almost   negligible   friction  factor  the  higher  velocity  curve 
coincides  with  the   ideal   curve. 


24 


11.  Explanation  of  Turbine  Rotation. — At  first 
glance  one  would  think  that  a  turbine  such  as  the  one  shown 
in  Figs.  7  and  8  would  rotate  in  a  clockwise  direction,  re- 
ceiving the  torque  components  on  the  slanting  sides  of  the 
cup  like  a  propeller  or  windmill.  Upon  placing  the  turbine 
in  a  moving  stream,  however,  it  will  be  found  that  it  ro- 
tates in  the  opposite  direction.  The  explanation  of  this 
is  comparatively  simple  after  having  previously  considered 
the  effects  of  eddy  currents.   On  the  right,  or  positive  half 
of  the  turbine,  two  torque  components  exist.  First,  a  veloci- 
ty force  is  exerted  against  the  open  face  of  the  cup  which 
may  be  imagined  as  being  filled  with  water  and  thus  presen- 
ting a  flat  surface  to  the  approaching  filaments.   Second, 
the  viscous  dragging  effect  existing  between  the  moving 
filaments  and  the  film  of  water  with  which  the  cups  are  coated 
exerts  a  pull.   On  the  left,  or  negative  half  of  the  turbine, 
three  torque  components  exist,  one  of  which  is  a  counter- 
clockwise or  positive  component.  Here,  a  velocity  force  is 
exerted  against  the  slanting  sides  of  the  cups.  Theoretical- 
ly this  resulting  torque  component  should  be  somewhat  smaller 
than  the  component  produced  from  the  same  kind  of  force  on  the 
right.  The  pull  due  to  the  viscosity  or  adhesion  exists 


here  also.  Then,  from  what  source  does  the  turbine  receive  its  ac- 
tuating torque?  The  real  force  which  turns  the  turbine  is  produced 
by  the  eddies  which  are  formed  behind  the  cups  on  the  left  side  due 
to  a  relative  motion,  or  difference  in  motion  between  these  cups 
and  the  filaments,  and  it  is  important  to  note  that  this  force  is  a 
positive  one.   Neither  is  this  component  of  small  consequence,  be- 
cause it  requires  an  appreciable  force  to  rotate  a  turbine  at  the 
speed  at  which  a  flowing  stream  does,  and  since  the  direct  veloci- 
ty forces  and  the  viscous  dragging  forces  practically,  or  very 
nearly  balance  each  other  on  the  two  sides,  it  remains  for  the  eddy 
forces  to  do  the  turning. 

Above  2.2  ft.  per  second,  a  slightly  different  condition 
exists.  The  same  forces  act  as  before,  but  less  cup  surface  or 
area  is  exposed  to  the  moving  filaments  since  they  cannot  enter 
the  inner  space,  which  means  that  the  number  of  active  filaments 
is  reduced  in  proportion.  However,  the  resulting  effect  of  these 
fewer  filaments  is  not  materially  reduced,  because  the  cups  are 
not  required  in  this  instance  to  buck  the  filaments  which  pre- 
viously worked  their  way  in  among  them  (the  cups).   On  the  left 
side  of  the  turbine,  there  exists  a  relative  motion  between  the  cups 
and  the  moving  filaments  with  the  resultant  production  of  eddy  cur- 
rents and  vacuous  spaces  in  the  rsar  of  the  cups,  just  as  before. 
Since  the  turbine  is  moving  too  rapidly  for  the  filaments  to  en- 
ter, that  dead  mass  of  water  already  within  the  cups  tends  to 
move  itself  over  to  the  left  and  rush  into  the  vacuous  spaces,  thus 
exerting  a  counter-clockwise  force.  This  movement  to  the  left  sets 


the  mass  eccentrically,  as  shown. 

The  more  radical  disturbance  of  the  filaments  approaching 
and  departing  from  the  turbine  is  simply  due  to  the   fact  that  thuy 
are  sucked  in  on  the  approach  and  hurled  off  at  the  departure  on  ac- 
count of  this  higher  velocity. 

Thus,  it  has  been  shown  that  the  existence  of  two  separate 
and  distinct  rating  curves — one,  the  starting  velocity  curve,  and  the 
other,  the  higher  velocity  curve— is  not  entirely  due  to  instrumen- 
tal friction,  but  is  largely  accounted  for  by  the  interference  of 
the  turbine  itself. 

12.   Other  Characteristic  Curves  for  Vertical  Shaft  In- 
struments.— Fig.  9  shows  the  surface  curve  for  a  Price  meter:  i.  e., 
a  rating  whose  data  was  observed  with  the  top  edge  of  the  turbine 
only  0.25  in.  below  the  surface  of  the  water.  Up  to  a  velocity  of 
1.2  ft.  per  second,  the  curve  is  not  unlike  the  ordinary  starting 
velocity  curve  for  this  type  of  meter.  However,  at  this  point, 
or  at  this  speed,  a  piling  up  effect  begins  to  appear  at  the  surface 
above  the  turbine  just  as  in  the  case  of  the  plate  and  the  rod. 
Fron  this  point  to  2.2  ft.  per  second,  the  slope  of  the  curve  is  less 
than  that  of  the  ideal  curve.  This  is  explained  by  the  fact  that 
the  higher  the  velocity,  the  greater  the  height  to  which  the  water 
is  piled,  and  this  piling  up  effect  absorbs  part  of  the  kinetic  en- 
ergy which  is  taken  from  the  active  filaments.  Consequently,  this 
means  a  proportionately  slower  rotation  with  the  resultant  lowering 
of  the  curve.  At  2.2  ft.  per  second,  however,  the  meter  first  ap- 
pears partly  freed  from  the  water,  and  from  this  point  on  the  water 
is  lifted  from  above  the  cups  at  an  increasing  rate  until  at  the 


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higher  velocities  the  turbine  is  simply  skimming  over  the  surface. 
The  curve  for  this  section,  as  shown,  is  characterized  by  a  steeper 
slope,  it  crossing  the  ideal  curve  at  a  velocity  of  3.2  ft.  per 
second . 

From  this  the  importance  of  the  depth  to  which  a  meter  is 
submerged  can  be  seen.   "One  can  expect  to  obtain  normal  results  on- 
ly when  the  meter  is  so  far  below  the  surface  that  the  static  head 
on  the  approaching  filaments  is  sufficiently  great  to  prevent  a 
transposition  of  any  of  the  velocity  energy."'   When  a  meter  is  at 
a  depth  less  than  this,  an  entirely  different  condition  is  confronted. 

Fig.  10  is  the  characteristic  curve  for  a  turbine  meter 
without  rigid  support.   "Without  rigid  support"  may  infer  either  a 
non-rigidly  supported  rod  meter,  or  a  cable  meter.  Up  to  3.5  ft. 
per  second,  the  curve  is  found  to  be  the  normal  rating  curve  con- 
sisting of  the  starting  velocity  curve  and  the  higher  velocity 
curve  which  coincides  with  the  ideal  curve  from  1.5  to  3.5  ft.  per 
second.  The  interference  factor  in  the  case  of  the  rigidly  supported 
meter  seems  to  be  a  minimum,  since  the  test  curve  and  the  ideal  curve 
coincide;  consequently,  any  alteration  in  the  shape  of  the  obstacle 
is  going  to  increase  this  interference  factor.   So,  it  will  be 
noted  that  the  test  curve  begins  to  fall  off  from  the  ideal  curve 
at  3.5  ft.  per  second,  because  it  is  at  this  point  that  the  rest- 
lessness of  the  meter  becomes  quite  apparent,  and  this  means  an  al- 
teration of  the  shape  of  the  obstacle  presented  to  the  oncoming 
filaments.  An  extension  of  this  upper  section  backward  across  the 


•'•"Current  Meter  Studies",  Ed.  J.  Hoff. 


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X-axis  indicates  a  negative  friction  factor  which  is,  of  course,  im- 
possible . 

15.  Horizontal  Shaft  Instruments. — In  Fig.  11  there  is 
shown  a  characteristic  rating  curve  for  a  horizontal  shaft  instru- 
ment, such  as  the  Haskell,  and  Ott.   This  curve  is  very  much  the  same 
as  a  normal  curve  for  a  vertical  shaft  instrument  in  that  it  is  made 
up  of  two  sections,  i.  e.,  the  starting  velocity  curve  and  the  high- 
er velocity  curve;  but  unlike  the  previous  type  curve,  this  one  does 
not  reach  the  ideal  .   One  advantage  of  this  type  meter  over  the 
turbine  type,  which  is  immediately  noticed,  is  a  shortening  of  the 
starting  velocity  curve — an  advantage,  because  as  long  as  the  veloci- 
ties are  within  the  zone  of  the  starting  velocity,  the  observations 
are  not  reliable  on  account  of  the  varying  friction  and  interfer- 
ence factors.  But  why  does  the  higher  velocity  curve  not  coincide 
with  the  ideal  curve  as  it  does  in  the  case  of  the  turbine  type? 
It  will  be  remembered  that  the  only  reason  why  the  turbine  meter 
curve  coincided  with  the  ideal  curve  was  because  the  higher  veloci- 
ties shut  out  the  filaments  from  within  the  turbine  itself,  and  thus 
reduced  the  interference  factor  to  a  constant  minimum.   In  the  case 
of  the  propeller,  or  horizontal  shaft  type  meter,  however,  this 
shutting  out  effect  can  obviously  not  be  accomplished.   No  matter 
how  fast  the  propeller  rotated,  these  filaments  would  always  find 
their  way  through  between  the  blades.  Hence,  the  vertical  dis- 
tance between  the  starting  velocity  curve  and  an  extension  of  the 


The  ideal  curve  for  a  horizontal  shaft  type  of  meter  is  drawn 
through  the  origin  and  parallel  to  the  higher  velocity  curve. 


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higher  velocity  curve    so  as   to  cross  the   X-axis   is    indicative   of 
instrumental  friction,  while   the  vertical  distance  between  the  high- 
er velocity  curve   and  the   ideal   curve   is    indicative   of  interference 
which  the  propeller   offers   to  the  moving   stream  filaments. 

Fig.   12   shows   a  characteristic   rating  curve   for  the   airme- 
ter  type   of  current  meter,    such  as  the  Fteley-Stearn,   and  Eckman. 
The    curve   really  shows   no  signs   of  a   single   redeeming  feature   for 
this  type.      It   is   simply  another  case  where  the  designer  has   com- 
pletely ignored  all   fundamental   principles   of  stream  flow,    interfer- 
ence,  etc. 

The   reader  should  first  be   reminded   of  some   of  the   physi- 
cal  features   of  these  meters.      Both  instruments   have  a  multi-bladed 
propeller  mounted   on  a  horizontal   shaft,   the   circumference   of  the 
propeller  being  bounded  by  a  metal  band.     The   shaft   is   pivoted   in 
a  yoke   whose   up-stream  edge   is   sharpened   in  stream  line   fashion. 
Bearing  these   facts   in  mind,   an  understanding  of  this  type   curve  will 
be  more  easily  arrived  at. 

The   starting  velocity  curve  extends   to  2.5   ft.   per   second. 
It  will  be   noticed  that  this   curve   crosses  the   ideal   curve   at   a  veloci- 
ty of  1.125   ft.   per  second.     This   crossing  is  due   to  the  effect   of 
the   proximity  of  the  yoke  to  the   front   of  the   propeller.     The   stream 
filaments   splitting   on  this  yoke   are   greatly  accelerated  as   they  move 
around  the   sides,   just  as   in  the   case   of  the   flat   plate   and  the   rod, 
and  they  strike   the  blades  with  this   increased  velocity  thus   causing 
a  higher  propeller   rotation  than  they  would   if  the  yoke  were   not 
present.     At   2.5   ft.   per   second,   the   propeller   is   swallowing  a  max- 
imum amount   of  water:   the   rim  around  the  blades   prevents   any  more 


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Table  2. 


Table  5. 


Rating  of  Hoff  Meter, 

Model  21,  Ko.  47.   Jan.  5,  1922. 


Course:  200  ft. 


Rating  of  Hoff  Meter, 

Model  21,  No.  48.   Jan.  23,  1922. 

Course:  200  ft. 


Time   in 

Revo- 

Revolutions 

Ft.  per 

Time  in 

Revo- 

Revolutions 

Ft.  per 

seconds  • 

lutions  . 

per  second. 

second. 

second. 

lutions  . 

per  second. 

second. 

124 

150 

1.21 

1.61 

73.2 

159 

2.732 

2.17 

83.5 

153 

1.83 

2.39 

64.5 

159 

3.1 

2.465 

75.2 

154 

2.04 

2.66 

51.5 

159 

3.88 

3.088 

84 

154 

1.83 

2.38 

38 

159 

5.26 

4.18 

68.8 

154 

2.24 

2.91 

74.2 

159 

2.691 

2.145 

62.5 

154 

2.46 

3.19 

75 

159 

2.665 

2.12 

55 

154 

2.8 

3.64 

85 

159 

2.35 

1.87 

44.8 

155 

3.46 

4.46 

114 

158 

1.76 

1.39 

38.5 

155 

4.02 

5.19 

111.2 

159 

1.8 

1.43 

38 

155 

4.07 

5.26 

151.5 

156 

1.32 

1.03 

95 

153 

1.61 

2.11 

154 

156 

1.3 

1.01 

97.5 

153 

1.57 

2.05 

120 

157 

1.67 

1.31 

111 

152 

1.37 

1.8 

131.2 

158 

1.52 

1.2 

122.8 

150 

1.22 

1.63 

142.3 

158 

1.41 

1.11 

122.6 

150 

1.22 

1.63 

148.4 

157 

1.35 

1.06' 

110 

152 

1.38 

1.82 

153.1 

157 

1.31 

1.02 

111 

152 

1.37 

1.8 

160.5 

156 

1.25 

.972 

106 

152 

1.43 

1.89 

170.  7 

156 

1.17 

.915 

111 

152 

1.37 

1.8 

177.3 

157 

1.13 

.885 

148 

150 

1.01 

1.35 

186.3 

157 

1.07 

.843 

104 

152 

1.46 

1.92 

225.7 

154 

.887 

.685 

161 

150 

.93 

1.24 

197.8 

155 

1.01 

.783 

174.5 

150 

.86 

1.15 

188.7 

156 

1.06 

.827 

198 

148.5 

.75 

1.01 

251.5 

154 

.796 

.613 

200 

148.5 

.74 

1. 

258.1 

153 

.775 

.592 

120 

153 

1.27 

1.67 

369.7 

137 

.541 

.371 

119 

152 

1.28 

1.68 

369.9 

141 

.54 

.381 

116 

154 

1.33 

1.73 

346.7 

142 

.577 

.41 

111 

151 

1.36 

1.8 

524.4 

126 

.382 

.24 

111 

153 

1.38 

1.8 

525 

115 

.381 

.219 

435 

134 

.459 

.308 

326.5 

139 

.613 

.426 

260.3 

146 

.769 

.561 

161.2 

154 

1.241 

.955 

260.2 

146 

.769 

.561 

372 

137 

.537 

.368 

384.6 

137 

.52 

.356 

439.6 

135 

.455 

.307 

353.8 

139 

.565 

.393 

380.2 

138 

.526 

.363 

296.8 

140 

.674 

.471 

472.3 

129 

.423 

.273 

37 


38 


water   from  passing  through.      So,   the  higher  velocity  curve  drops, 
and   crosses  the   ideal  curve   at   a  velocity  of   3.333  ft.   per  second. 

Fig.   13   shows  the   rating   curve   for  a  Hoff  meter,  model 
21,   No.  47.     This   curve    is   not  unlike  the   characteristic   curve   for 
the  horizontal  shaft  type   of  meters   shown  in  Fig.   11;    consequently, 
no  explanation  need  be  made.     The  velocity  of  the   car  cculd  not  be 
carried  below  1   ft.   per  second   at  the  time   the   rating  was  made,    so 
the   curve  does   not   show  what  takes   place   at  the   lower  velocities. 
After  making  a  slight   change   in  the   spindle    (and  changing  the   num- 
ber  of  the  meter  to   No.   48),   another  rating  was  made.      The   re- 
sultant  curve    is   shown  in  Fig.   14.      One   notable   advantage   over  the 
Ott  and  Haskell  meters  which  this   curve  indicates    is   a  marked  de- 
crease  in  the   starting  velocity.      It   is  this   improvement  which 
makes  the  Hoff   instrument   particularly  well  adapted  to  the   low 
velocities  encountered   in  irrigation  investigations. 

Fig.   15   shows  the   surface   curve   for   one   of  the  Hoff  trial 
meters    .     The  data  for  this   curve,   like   that  for  the   curve    in  Fig. 
9,  was   observed  with  the  top  edge   of  the  meter  only  0.25   in.   below 
the   surface   of  the  water.     At  the   point  where   the    starting  veloci- 
ty curve   ends,   a  piling  up  of  the  v,-ater  at   the   surface   over  the  me- 
ter  is   apparent.     As  before,   a  certain  amount   of  the  velocity  ener- 
gy is   consumed   in  lifting  the  water;   and  as   a  result,    less  velocity 
energy   is   imparted  to  the   propeller  blades,   and   the   curve  begins  to 
drop  down  from  the   ideal   curve.      In  this    case,   the  meter   is   at  no 
time   entirely  free   from  the  water,   and   consequently  the   curve  does 


This   meter  was   one   of  Mr.  Hoff's   experimental  meters   of  the  hori- 
zontal  shaft  type  which  he  used   in  the   development   of  his   present 
meter. 


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40 


not  rise   again  as   it   does   in  the   case   of  the   Price  meter  at  the   sur- 
face. 

14,     Summary. — Before   leaving  this   subject,   the   outstanding 
features   should  again  be   pointed   out. 

(1)  Every  normal   rating  curve   is  made   up  of  two   separate 
and  distinct   curves — the   starting  velocity  curve,    and  the   higher 
velocity  curve — each  of  which  has   its    own  independent  equation. 

(2)  TWO  factors   affect   the   characteristics   of  a  rating 
curve:   the   instrumental  friction  factor,   and  the   interference   factor. 
The   interference    factor   causes   the   test   curve  to  lie  below  the   ideal 
curve;    and  the   instrumental  friction  factor  causes   the   starting 
velocity  curve  to  break  from  the   higher  velocity  curve   at  the 
velocity  at  which  that  factor   ceases   to  be   a  constant. 

To  be  more   specific:    in  a  vertical   shaft  turbine  meter, 
the   starting  velocity  curve   rises   from  a  point   at  the   right   of  the 
origin  on  the  X-axis   to  the  ideal   curve.     When  the   turbine   just  be- 
gins to  rotate,   the  almost  negligible   friction  factor  is  a  maximum. 
At  2.2   ft.   per  second,    it   is  a  minimum  and  a  constant.     Also,   at 
the    start,  the  very  appreciable   interference   factor  is   a  maximum; 
and  at  2.2   ft.   per  second,    it  has  been  reduced  to  an  almost 
negligible  minimum  which  is   a  constant.     The   sum  of  the   instru- 
mental friction  and   interference   factors  makes   the   starting  velocity 
curve   lie  below  the   ideal  at  the   start.     At  2.2  ft.   per   second, 
both  factors   are  practically  negligible,   and  are    constant;   hence } 
above   this   velocity  the   higher  velocity  curve   and  the   ideal   curve 
are   one  and  the   same   thing. 


1 
•  a,;    »    • 


41 


In  the   case   of  the  horizontal  shaft   propeller  meter,  the 
starting  velocity  curve    rises   from  a  point  at  the   right   of  the   ori- 
gin on  the  X-axis   to  a   point  where    it  merges  with  the   higher  veloci- 
ty curve,   this  point  being  below  the    ideal   curve.     '(Then  the  propel- 
ler first  begins   to  rotate,  the   almost  negligible   friction  factor 
is   a  maximum.     At   1  ft.    per  second,    it   is  a  minimum  and  a   constant. 
It   is  this   friction  factor  which  is    responsible   for  the  two   separate 
curves.     The  interference  factor,    in  this  case,   is   the  factor  which 
holds   the  test  curve  below  the   ideal  curve,   because   at  no  time    is   it 
negligible,   but,   above   1  ft.   per   second,   it  is   always   a  small   con- 
stant  factor. 

(3)  The   reliability  of  observations  made   in  the   zone   of 
the   starting  velocity  is   to  be  questioned,  because   of  the  varying 
friction  and   interference   factors. 

(4)  It   is   important  that  the  meter  be   immersed  to  a 
depth  at  which  the    static  pressure   on  the   filaments   approaching  the 
turbine   or  propeller   is   sufficient  to  present  the   piling  up  of  the 
water  above.      In  general,  the  depth  of  submergence   is    proportional 

to  the  volume   of  the  meter.     Mr.  E.    C.  Murphy     states  that   0.5   ft. 

2 
is   sufficient  for  the   small  Price  meter]   Mr.   F.   C.   Scobey     states 

that  0.3  ft.   is   sufficient. 

(5)  If  a  rating  curve   at  any  point   crosses  the   ideal 
curve,    it    is   an  indication  of  either  a  faulty  rating,    or  a  poorly 
designed   instrument. 


Engineer,   U.   S.   Geological  Survey. 

Irrigation  Engineer,    Office   of  Experiment  Stations. 


• 


C.      Supplementary  Tests^ 

15.  Purpose. — The   results   of   four   sets   of  tests  will  be 
set   forth  in  this   section.     The   results   of  the   first  three   sets 
are   included  so  as   to  show  that  what  has   been   said  about  the  for- 
mation of  eddies   about  obstacles   and  their   effects   is  directly 
applicable   to  current  meters.      Owing  to  the   general  nature   of  the 
tests,   and  to  the   uncertainty  of   the  behavior  of  eddy  currents, 

no  rigid  conclusions   can  be   drawn;   but  general   statements  may  be 
made,  which  the  writer  trusts  will  be   of  some   value. 

The   fourth  test  was  designed  to  prove   that   the  Hoff 
theory  of  interference   is   correct. 

16.  Effects   of  Wires,   Rods,   Yokes   and   Cables   on  Current 
Meter   Operation. — As   shown  in  Sections   7  and  8,   the  velocity   of  the 
water  flowing  around  any  obstacle   is  at   some   points   increased,  while 
at   others   it   is  decreased.     A  corresponding  transposition  of  the 
forms   of  internal  energy  was   also  noted.     These    statements   are 
substantiated  by   some   of  the   following  tests. 

If  a  wire   C.06   in.   in  diameter   is   held  6   in.   in  front 
of  a  Price  meter,   the   rotation  is   reduced  3  per  cent. 

A  rod  0.5   in.   in  diameter  suspended  9   in.   in  front   of 
a  turbine  meter   in  water  moving  at  a  velocity  of  4  ft.   per  second 
will   reduce   the   rotation  about   16  per   cent;   at  2.5  ft.   per  second, 
about   13  per   cent.     The   same   rod   9   in.   in  rear  of  a  turbine   at 
4  ft.   per   second  will   cause   a  decrease   in  rotation  of  about   3 
per   cent;   at  2.333   ft.   per   second,   about  9  per  cent. 

Reversing  the  Price  meter  so  that  the  yoke   points   up- 
stream will   cause  an  increase   of  about   10  per  cent  in  the  turbine 
rotation. 


Table  4. 

Table  of  current  meter  ratings  showing  the  relation  between  cable  and  rod 

suspension.  Ratings  made  at  the  Hydraulic  Labratory,  Colorado  Experiment 

Station,  Ft.  Collins,  Colorado. 


Rating 

No.     Date  ' 

Suspension 

Weight 

Equation 

Mean  Equation. 

Gurley  Meter 

No.  1728 

471 

6-21-17 

Rod 

V 

— 

2 

.191R 

+ 

0 

.030 

518 

8-16-17 

it 

V 

= 

2 

.188R 

+ 

0 

.023 

V  =  2.19R  +  0.025 

502 

8-14-17 

4ft.  cable 

Single 

V 

= 

2 

.249R 

+ 

c 

.016 

503 

n 

5ft.  c&ble 

" 

V 

= 

2 

.247R 

4- 

0 

.035 

504 

* 

6ft.  cable 

• 

V 

= 

2 

.277R 

4- 

0 

.022 

505 

• 

7ft.  cable 

n 

V 

= 

2 

.256R 

+ 

0 

.014 

506 

n 

8ft.  cable 

it 

V 

= 

2 

.274R 

4- 

0 

.004 

507 

n 

9ft.  cable 

n 

V 

= 

2 

.245R  + 

0 

.030 

508 

8-15-17 

10ft.  cable 

n 

V 

• 

2 

.261R 

4- 

c 

.012 

509 

n 

lift,  cable 

it 

V 

= 

2 

.258R 

4- 

0 

.013 

510 

n 

lift,  cable 

Double 

y 

3S 

2 

.294R 

4- 

0 

.038 

511 

it 

8ft.  cable 

n 

V 

= 

2 

.268R 

4- 

0 

.042 

512 

n 

5ft.  cable 

it 

V 

= 

2 

.286R 

4- 

0 

.012 

V  =  2.26R  -t-  0.025 

Gurley 

Meter 

No.  51 

347 

3-31-16 

Rod 

V 

_ 

2 

.29  R 

+ 

c 

.04 

453 

3-30-17 

n 

V 

= 

2 

.295R 

+ 

0 

.055 

567 

10-8-17 

it 

V 

= 

2 

.299R 

4- 

0 

.035 

V  -  2.30R  +0.04 

643 

10-29-18 

Cable 

Double 

V 

= 

2 

.401R 

4- 

c 

.043 

V  =  2.40R  +0.04 

Gurley  Meter 

No.  1314 

109 

9-21-15 

Rod 

V 

= 

2 

.193R 

+ 

0 

.040 

112 

9-24-15 

n 

V 

= 

2 

.188R 

4- 

0 

.015 

261 

11-8-15 

it 

V 

= 

2 

.196R 

4- 

0 

.033 

468 

6-21-17 

it 

V 

• 

2 

.184R 

4- 

c 

.023 

V  =  2.19R  +  0.03 

113 

9-24-15 

Cable 

Single 

V 

= 

2 

.262R 

4- 

c 

.015 

V  =  2.26R  +  0.02 

Lietz  Meter 

No.  8374 

107 

9-20-15 

Rod 

V 

_ 

2 

.362R 

4- 

0 

.025 

264 

11-9-15 

n 

V 

= 

2 

.346R 

4- 

0 

.045 

266 

" 

it 

V 

= 

2 

.352R 

-"- 

0 

.060 

V  =  2.35R  +  0.05 

108 

9-20-15 

Cable 

Single 

V 

= 

2 

.356R 

4- 

0 

.049 

V  =  2.36R  +  0.05 

Lai  lie 

Meter 

No.  300 

296 

11-15-15 

Rod 

V 

= 

2 

.241R 

4- 

0 

.041 

V  =  2.24R  +  0.04 

306 

11-16-15 

Cable 

Single 

V 

= 

2 

.29  R 

4- 

0 

.06 

V  =  2.29R  +  0.06 

Gurley 

Meter 

No.  1640 

358 

5-8-16 

Rod 

V 

- 

2 

.20  R 

4- 

0 

.02 

V  =  2.20R  +  0.02 

359 

it 

Cable 

Single 

V 

= 

2 

.22  R 

4- 

0 

.02 

V  =  2.22R  +  0.02 

44 


Table   5. 


Zahlenta.fel   8. 


Xo.      Means    of    ! 


, 


Meter   vo.   289/11,    Ott  catalog  VII,   propeller  b: 
heavy,    cylindrical   contour. 


1.      Flat    iron  bar,    7  x  50  •     .  . 

Cable,    9  mm.    di^r.eter.      (;' 

Top  of  railroad   rail,      m.   loi  crted  by 

two  cables.      (!•••• 
4.       Ire-.  (242    -     . 

n  •  r   —* 


C.92P 
0.934 

O.S44 


' 


n 


VVVifcm 


••ntaf-1   9. 


Meter  Xo.    r<:               ,             -'Inr   of  conicnl   form,   22   cm.  diameter, 

1.  ir   of  ova]                                            x  5.4  cm.  0.679 

2.  Cable    with  b«  0.685 

3.  Iron  pipe,   4.5   cm.    diameter.  700 

,    7 . 5   c                        r .  0 . 706 

Zahentafel   10. 
Large   I  r  ice   meter,    I'D.    136,    cup  .turbir.* . 

1.  Free    suspension  by  cable.  0. 

2.  Iron  rod,   2   cm.   diameter.  0.95 

3.  Iron   rod,   4   cm.   diameter.  0.990 


45 


Table   4  is  a  summary  of  a  series   of  tests  made  at  the 
Hydraulic   Labratory,   Colorado  Experimental   Station,   Ft.   Collins, 
Colorado.     These   tests  were   carried   out   in  an  attempt  to  find  some 
definite   relation  between  the   rating  of  a  cable  meter  and  the   rating 
of  the   same  meter   suspended  by  a  rod}  however,   they  will   serve   another 
purpose   quite   as  well. 

These   ratings  were  made  before  the  advent   of  the   Hoff 
theory,    and   consequently  disregard  the   fact  that   a  rating   curve  is 
divided  up  into  two  separate   sections;   however,   this  erroneous   idea 
will   not  materially  affect  the    conclusions   to  be  drawn  in  this  in- 
stance,   since  all   the   curves  were  plotted   in  the    same   manner,    i.  e., 
a   straight   line   through  as  many  points  as   possible. 

With  the  exceptions   of  the   test   on  the   Gurley  meter  No. 
1314  and  the   test   on  the  Lallie  meter  No.   300,  the   only  deviation 
between  the  mean  rod  and   cable   equations   appears   in  the    slope   fac- 
tor.     In  the  two  exceptions   noted,  there   is  a  difference   of  0.01 
and  0.02   in  the   friction  factor,   respectively;   but   since   these 
differences   are   in  the    opposite  directions,    it  would  be  quite   pos- 
sible to  attribute  them  to  personal  errors. 

Table   5   is   a  reproduction  of  Tables   8,   9  and   10  from 
Dr.   Schmidt's   article    .     These  tables  were  compiled  from  the   ratings 
of  current  meters   supported  by  various  means,    some  by  cable,   and 
others  by   rods   of  different  cross   sections.     With  the   same  meter, 
a  wide   variation  in  the   coefficient  k,   the    slope   factor,    is   noted. 
The   coefficients   should  not  differ,   since   the    same  meter  is  being 
used,  but   it   is   the   change   in  the   interference  factor — the   change 
in  the   shape   of  the   non-rotating  parts   due   to  the   change   in  the 


See  bibliography. 


46 


means   of  support — that   causes   the   resultant  variation. 

What  general   conclusions   can  be  made  now  after  having 
studiid  these  tables   carefully?      In  the   first  place,    it  has  been 
shown  that  by  the   introduction  of  obstacles,  the   resulting  distur- 
bance   of  the   filaments   and  the  alteration  of  their  forces  material- 
ly affects   the   rotation  of  the  meter.      In  other  words,   any  obstacle 
in  a   stream  alters   the   internal  energy  of  the   flowing  filaments, 
just   as   in  the   case   of  the   flat  plate   and  the   rod,    and   if  these 
affected  filaments   are  the   ones   causing  rotation,    the   standard 
rating  equation  is  not  applicable,   since   it  was   determined  after 
a  rating  in  still  water  where  apparently  undisturbed  parallel   . 
filaments   exist. 

Second,   these    results,   though  rather   loosely  related  to  ore 
another,  are   responsible   for  this    statement:     The   slope   of  a  rating 
curve  depends   not   only  upon  the   pitch  of  the   propeller  or  turbine, 
if  such  a  term  may  be   applied  to  a  turbine,  but  also  upon  the   inter- 
ference which  the   complete  meter   offers  the   oncoming  filaments — 
including  all  protecting  devices   such  as  wires,    rods,  etc.,  yokes, 
tails,  weights,   suspension  rods   and   cables,   spindle  housings,   sup- 
ports, binding  posts,    contact  wires,   etc.,   etc.      The   importance   of 
this   statement  cannot  be    overestimated.      In  reply  to  this    objection, 
one  will   say  that  these   factors   are   all   covered   in  the   rating.     True 
enough,  but   field   conditions  are   so  radically  different   from  the 
ideal  rating  conditions   that   an  operator  never  knows  how  close   his 
results  are   going  to  be,  because   in  the   former   instance   parallel 
stream  filaments   never  exist,  while   in  the   latter,   it   is   not  un- 
reasonable to  assume   that   they  exist   at   all  times,   and  a  change   in 
the  direction  of  a  filament  flowing  around  an  obstacle  alters   the 


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49 


Table   6. 

Rating   of  Price   Meter,  Model   220. 
Dec.   30,   1921. 


Table  7^ 

Rating  of  Price  Meter,  Model  142. 
Doc.  30,  1921. 


Meter  suspended  on  a  rod  with  an  "L"  shaped  end  thus  causing  the  meter  to  operate 
as  a  horizontal  shaft  meter  rather  than  a  vertical  shaft  instrument. 


Course:  120  ft. 

Time      in     Revo- 
seconds,      lutions 


Revolutions     Ft.   per 
per  second,     second. 


Course:  120  ft. 

Time   in  Revo-     Revolutions  Ft.  p«r 
seconds,   lutions.   per  second,  second. 


Base  end  up-stream 

,  with  base. 

43.2 

31.6 

.731 

2.77 

26.5 

4.4 

.166 

4.52 

20.9 

31.6 

1.511 

5.74 

56 

4.3 

.077 

2.14 

50.4 

31.5 

.626 

2.38 

102.6 

2.2 

.021 

1.17 

81.7 

30.6 

.374 

1.47 

22.7 

4.4 

.194 

5.28 

117.8 

29.3 

.249 

1.02 

Base 

end  up-stream, 

without 

base 

17.8 

29.3 

1.645 

6.74 

58.2 

31.4 

.539 

2.06 

103.3 

27.6 

.267 

1.06 

25.7 

31.4 

1.221 

4.66 

127.9 

26.3 

.206 

.94 

20.5 

31.4 

1.531 

5.85 

96.3 

27.3 

.283 

1.24 

71.7 

31.1 

.433 

1.67 

62.4 

28.4 

.455 

1.922 

111.5 

29.8 

.267 

1.07 

43.6 

28.9 

.662 

2.75 

19.3 

31.6 

1.638 

6.21 

24.8 

29.3 

1.181 

4.83 

96.7 

30.2 

.313 

1.24 

16.8 

31.5 

1.873 

7.13 

122.8 

29.3 

.239 

.98 

Base 

end  down-stream,  with 

base. 

134.8 

29.2 

.217 

.892 

28. 

.6 

1.211 

4.19 

135.1 

30.2 

.223 

.886 

21.1 

34.6 

1.639 

5.68 

93.2 

32.2 

.345 

1.29 

76*9 

33.8 

.439 

1.56 

49.6 

34.2 

.69 

2.42 

129,6 

31.3 

.242 

.925 

25.1 

34.2 

1.362 

4.78 

72.8 

33 

.453 

1.65 

Base 

end  down-stream 

,   without  base  . 

\ 

31.9 

33.3 

1.043 

3.76 

115,1 

31.  '8 

.276 

1.04 

28.8 

33.3 

1.156 

4.16 

61, 

.32.5 

.532 

1.96 

18.9 

33.3 

1.76 

6.34 

133,.  7 

31.2 

.233 

.9 

42.3 

33.3 

.787 

2.84 

28,9 

32.9 

1.138 

4.15 

64.7 

32.4 

.501 

1.85 

53,.  2 

32.9 

;618 

2.25 

109.1 

30.2 

.276 

1.1 

21.9 

32.9 

1.502 

5.47 

152.3 

27.3 

.179 

.79 

123 

29 

.236 

.97 

50 


situation  entirely.      In  conclusion,   it  may  be   said  that   the    lesser 
the   number  and   size   of  the   non-rotating  parts,   and  the   smaller  the 
size   of  the   rotating  member   itself,   the   nearer  has  the  designer 
approached  the   ideal  meter. 

17.     Tests   of  Price  Meters   as  Horizontal  Shaft  Meters. — 

1  2 

The   results   from  tests  made   on  Price  meters   No.   220     and  142     are 

plotted   in  Figs.   17  and  18,   respectively. 

In  these   tests,   the   meter  was   suspended  from  an  ordinary 


Table   8 

• 

(1) 

(2) 

(3) 

(4) 

(5) 

Interference 

Interference  plus 

Friction 

Figure 

Slope   Factor 

Factor 

Friction  Factor 

Factor 

17   (a) 

3.772 

.06 

.22 

.16 

17   (b) 

4.073 

.05 

.2 

.15 

17   (c) 

3.464 

.06 

.22 

.16 

17   (d) 

3.596 

.09 

.23 

.14 

18   (a) 

31.75 

.15 

.8 

.65 

18   (b) 

3.802 

.06 

.34 

.28 

18   (c) 

3.479 

.06 

.17 

.11 

18   (d) 

3.618 

.05 

.37 

.32 

rod  equipped  with  a  "L"   joint   on  the  end  so  that  the  turbine    shaft 
was   horizontal.     The  yoke   in  each  case  was   turned  up. 

These   curves  will  be   discussed   in  pairs,   as   fol.:   type   220, 
base  end  up-stream,  with  and  without  base;   base  end  down-stream, 
with  and  without  base;   type   142,  base  end  up-stream,  with  and  with- 
out base;   base  end  down-stream,  with  and  without  base.     Table   8 
shows   parts    of  the   rating  equations   listed   in  the   order   in  which 
the   curves   are  to  be  discussed.     The   factor  added  to  the   slope 
factor   for  the  higher  velocity  curve   is   indicative   of  interference. 


Concentric  foot  plate.      (Nos.   142  and  220  are   test  numbers  ) 

^Eccentric   foot  plate.        (referring  to  the   two  types    of  model  618.) 


51 


The   factor  added  to  the    slope   factor  for  the   starting  velocity  curve 
includes   the   instrumental  friction  factor  and  the   interference   fac- 
tor.    Therefore,  the  difference  between  columns   (3)   and   (4)   gives 
the   instrumental  friction  factor   for  the  meter,   shown  in  column  (5). 

The   slope   of   curve   17    (a)    is   steeper  than  that   of  17    (b). 
This   is   quite  unexpected,    since,  when  the   plate   is   removed,  more 
cup  surface   is  presented  to  the   oncoming  stream  filaments;   but  why 
is   the   rotation  almost    the  same   in  both  cases?      It   is   because   of 
the   fact  that,   in  the   first   case,   the  turbine   is   rotating  at   an  ab- 
normal   speed   on  account   of  the  water  being  accelerated  as   it  passes 
around  the   edge   of  the   plate.      Neither  is   the   turbine    required  to 
buck  the  filaments   because  the   plate  holds  them  back. 

The   interference   factors   in  this   series   of  tests   are   not 
comparable,   because   in  each  instance   they   are   affected  by  a  change 
in  the  non-rotating  element.      In  other  words,    in   (a)    the   foot  plate 
is   up-stream  vnLth   the   supporting  rod   in  the   rear,  while   in   (c)    just 
the   opposite   arrangement  exists;    in   (b)   the   supporting  rod   is   in  the 
rear,  while   in  (d)   it   is   in  front. 

Curve   17  (b)    shows  a  smaller  friction  factor  than   17  (a). 
This   is   on  account   of  the  higher   slope   in  the   former  case — the   fast- 
er a  turbine  rotates,  the   less  appreciable  the   friction. 

The  same  explanation  for  the  slope  and  friction  as  given 
above  will  apply  to  curves  17  (c)  and  (d). 

Due  to  the  eccentric  foot  plate  on  models  No.  142,  curve 
18  (a)  has  a  very  small  slope,  this  plate  covering  almost  one-half 
of  the  cup  surface,  and  thus  causing  an  unbalanced  torque  which  ac- 


52 


counts  for  a  friction  factor  much  greater  than  the  one  in  18  (b) . 

Curve  18  (c)  has  a  steeper  slope  than  18  (d).  Here,  the 
total  area  is  presented  to  the  oncoming  filaments  in  both  cases J 
but  with  the  base,  the  filaments  are  accelearted  in  passing  around 
the  edge  with  a  resultant  higher  rotation. 

The  friction  factor  in  (d)  is  greater  than  that  in  (c). 
The  writer  can  offer  no  plausible  explanation  for  this  fact — pos- 
sibly, personal  errors  are  responsible. 

Each  of  these  curves  fall  below  the  ideal  curve,  just  as 
in  the  case  of  a  propeller  type  of  meter.  Also,  each  curve  is  made 
up  of  the  two  sections,  the  same  as  any  normal  rating  curve.  These 
tests,  then,  are  eight  separate  and  conclusive  proofs  for  the  valid- 
ity of  the  Hoff  theory  of  interference:  it  is  the  minimizing  of  the 
interference  factor  in  the  case  of  a  Price  meter  which  is  largely 
responsible  for  the  coincidence  of  the  higher  velocity  curve  with 
the  ideal  curve . 

III.   REQUIREMENTS  FOR  IDEAL  CURRENT  kETER  MEASUREHBRTS. 

18.  Requirements. --The  requirements  for  ideal  current  me- 
ter measurements  may  be  enumerated  as  fol.: 

1.  A  conscientious  operator. 

2.  Parallel  stream  filaments  without  viscosity. 

3.  A  meter  satisfying  the  fol.  conditions: 

a.  Rigidly  suspended. 

b.  Meter  parts  shall  not  disturb  stream  fila- 
ments in  any  manner. 

c.  Propeller  or  turbine  infinitely  •small. 

d.  Frictionles^  bearings  and  electrical  contacts. 


53 


19.  Possibility  of  Realizing  Ideal  Requirements . — 
(l)   Little  need  be  said  here  concerning  the  operator  .  Even  with 
a  perfect  meter,  certain  precautions  must  be  observed  if  accurate 
results  are  to  be  obtained. 

(2)  This  requirement  is  out  of  the  question.   In  the 
first  place,  parallel  stream  filaments  never  exist.  Prof.  Hele 
Shaw,  and  a  few  other  prominent  scientists  have  succeeded  in  pro- 
ducing parallel  stream  lines  in  perfectly  smooth,  round  glass  pipes 
where  the  velocity  was  below  the  critical  value,  but  it  is  impos- 
sible for  these  ideal  currents  to  exist  in  flowing  streams  and 

.canals.   It  is  not  impossible,  however,  to  design  a  meter  whose 
rotating  element  will  be  impelled  by  only  those  components  of 
stream  filaments  perpendicular  to  the  base  plane  of  measurements. 
This  requirement  is  more  nearly  realized  in  the  Hoff  meter  than  in 
any  other  current  measuring  instrument.   Section  23  will  treat  of  this 
phase  of  the  Hoff  meter  in  detail. 

In  the  second  place,  no  fluid  is  entirely  devoid  of  vis- 
cosity. 

(3)  Now,  as  to  the  requirements  of  the  meter  itself. 

Only  under  the  most  favorable  conditions  can  it  be  rigidly  suspended. 
There  are  times  when  the  cable  suspension  must  be  resorted  to.   In 
these  cases,  the  reliability  of  the  observations  lies  largely  in  the 
hands  of  the  operator. 


"River  Discharge",  by  Hoyt  and  Grcver,  is  recommended  to  t!e  obser- 
ver as  being  a  very  good  handbook. 


54 


Any  obstacle   in  a   stream  is   going  to  disturb  the  moving 
filaments.     Consequently,   it   should  be  the  designer's   aim  to  elimi- 
nate  as  many  dispensable   parts   as   possible,   and  to  reduce   all  the 
remaining  parts   to  trie  least   size.     Wherever  possible,   these   parts 
should  be   stream  lined   so  as   to  minimize  the   disturbance. 

For  the    same   reason,   the   propeller  should  be   as   small  as 
possible.     This    is  an  especially  important  factor  where   irrigation 
ditches  are  to  be   gaged,   because,   here,   the  velocities   are  very  low, 
and  the   cros^s   sectional  areas   small.     With  this   combination  of  con- 
ditions,  the   observer  has   an  impossible   task  if  he   is   using  a  meter 
of  large   dimensions.      It  will  be  remembered  that  a  disturbance    is 
more  widely  felt  where   the  velocities   are   low.      So,    in  a  canal, 
unless   the  meter   is   very  small,   a  very  radical   disturbance  will  be 
produced,   and  the  gaging,   at   the   bsst,    can  be   nothing  more  than  an 
approximation. 

With  a  small  propeller  or  turbine  the  moment   of   inertia 
is  materially  reduced,   and   a  shortening  of  the    starting  velocity 
curve   is   effected.     This   is   one   of   the   objections   to  the   large 
Price  meter.      Its  turbine,  when  set   in  motion  with  the  hand,  will 
rotate   for  4  minutes,  thus   indicating  a  large  moment  of  inertia. 
A  meter   of  this   type  will   not  be   as   sensitive  to  pulsating  flow  as 
a  meter  whose    rotating  element  has   a  smaller  mass. 

In  the  best  meters,    instrumental   friction  is   an  almost 
negligible   factor.     This   fact   is  borne   out  by  a  test  which  will  be 
discussed   in  Section  22.     The  Hoff  meter,   model   22,   is   equipped  with 
a  5  to  1  counting  device  which  is   simply  a  small  pinion  worm  driven 
from  the   propeller   spindle.     This   necessitates   the  use   of  a  second 


t  •! 

' 


56. 


Table  9. 

Rating  of  Hoff  Meter,  Model  22.  March  3,  1922. 
Course:  57.65  ft. 
1:1  counter. 


Time   in  Contacts  . 
seconds  . 

Revo- 
lutions . 

Revolutions 
per  second. 

Ft.  per 
second. 

21.3 

46 

2.161 

2.73 

17.6 

46 

2.612 

3.28 

13.7 

46 

3.36 

4.215 

11 

46 

4.178 

5.245 

12.8 

46 

3.595 

4.515 

16 

46 

2.878 

3.608 

20 

45.8 

2.29 

2.884 

23.2 

45.6 

1.969 

2.486 

27.9 

45.4 

1.627 

2.067 

35 

45 

1.286 

1.65 

45 

44.5 

.99 

1.282 

45.7 

44.4 

.974 

1.263 

52.5 

44.4 

.846 

1.099 

57.5 

44.4 

.772 

1.003 

64.8 

44 

.679 

.891 

96 

42.2 

.439 

.601 

105.7 

42.2 

.399 

.547 

138.7 

41.4 

.299 

.416 

5:1  counter. 


11 

9.2 

46 

4.178 

5.245 

9.7 

9.2 

46 

4.74 

5.945 

8.4 

9.2 

46 

5.475 

6.868 

14.5 

9.2 

46 

3.172 

3.979 

18.2 

9.2 

46 

2.527 

3.17 

With  gear  wheel   removed.      1:1   counter, 


13.5 

15.7 

18.4 

20.6 

21.2 

24.6 

36.2 

67 

98.5 


46 

3.407 

4.271 

46 

2.932 

3.672 

46 

2.502 

3.137 

46 

2.234 

2.8 

45.8 

2.161 

2.72 

45.7 

1.858 

2.344 

45 

1.243 

1.594 

44.2 

.661 

.861 

42.2 

.429 

.586 

57 


contact  point.     The    results   of  a  rating  of  the   complete  metor   com- 
pared with  those   obtained  from  a  rating  after  the   gear  had  been  re- 
moved showed  almost   identical  equations.      In  the   latter  case,   the 
friction  in  the   gear-spindle  bearing,   the   friction  between  the   gear 
and  worm,   and  the    friction  between  the   gear  and   contact  point  had 
all  been  removed,   but  their  sum  was   so  small  that  the   rating  equation 
was   scarcely  affected.     See  Figs.    16   and   19. 

Obviously,    it   is    impossible    to  design  a  perfect  meter. 
However,   the  designer  should  not  be   satisfied  until  he  has  done  the 
best  possible.     A  few  of  the   requirements   can  be  attained;    for  those 
which  cannot  be   attained,   each  detail   should  be   studied,  and   the   closest 
approach  to  the   ideal   should  be  made. 

Aside   from  these   requirements  which  have  to  do  with  the 
actual   operating  characteristics,  the   ideal  meter   should  be   fool- 
proof.    The  metal  parts   should  be   strong  and  durable,   and   of  a  non- 
corrosive  material.     Each  detail   should  be   of  the   simplest  design, 
and  accessible.     The  bearings   should  be   simple,   and  require   only  a 
very  occasional   oiling.      The   electrical   contacts    should  also  re- 
ceive no  little   attention  from  the  designer,  because  this   is   in 
many  cases   the  most   frequent  source   of  trouble.      In  short,   the 
meter  should  be  simple,   and  yet   complete]    it   should  be   strong, 
and  yet  the  parts   should  not  be  massive;   and  above  all,   access   to  any 
part   should  be   readily  gained,   so  that  an  operator   in  the   field 
equipped  with   only  a  screw  driver  and  a  pair   of   pliers  would  be 
able  to  dismantle   it,   remedy  any  apparent  trouble,   and   reassemble, 
yet   it  should  be   so  fool-proof  that  after  any  repairs   or  adjustments 
the   rating  would  not  be   altered. 


58 


IV.      THE   VSRTICAL  SHAFT  TUP.BI  .:  V".   THE  HORIZONTAL  SHAFT 

PROPELLER  METER. 


20.     Advantages   of  the  Vertical  Shaft  Turbine  Type  Meter. — 

1.  Strong,  well  built. 

2.  Utilization  of  eddy  forces. 

3.  Negligible   friction  factor. 

4.  Test   curve   coincides  with  ideal   curve. 

(1)  Most   of  the  turbine  meters,   and  this    is   especially 
true   of  the   Price  meter,   are  very  well  built,    and  are    strong  and 
durable.     This   is   certainly  an  advantage  because   an  instrument   is 
sure   to   receive  a   certain  amount   of  abuse   and   rough  treatment  even 
in  the   hands   of  the  most   careful   operator. 

(2)  This   type   of  meter  has  the   advantage   of  utilizing  the 
eddy  forces  which  are   produced  about   its    oddly  shaped   turbine.     The 
writer  does   not  mean  to  state   that  eddy  forces   are   advantageous. 
They  are   not;    in  fact,   they   are   a  constant  source  of  uncertainty, 
but  the   fact  that  the  turbine  makes  use   of  these   forces   is   another 
point   in  its   favor . 

(3)  The   vertical   shaft   instruments   are   ordinarily  equipped 
with  more   or   less  delicate  bearings,  which,  when  in  good   condition, 
are   almost   fricticnless;   but  they  are   often  badly  worn  or  out   of  ad- 
justment,   and   it   is  under  these   conditions  that  they  become   trouble- 
some,  and  produce   an  appreciable   friction  factor. 

(4)  The   higher  velocity   curve   of  a  turbine  meter   in  good 
repair  ordinarily  coincides  with  the   ideal    curve.     This   may  seem  an 
advantage  to  some,   but   it   i s  the  writer's   opinion  that  when  the   test 
curve   is   a  straight   line   and  very  near  the   ideal   curve,    it    is   just 
as  well. 


59 


21.  Disadvantages  of  the  Vertical  Shaft  Turbine  Type 
Meter. — 

1.  Worn  bearings. 

2.  Bent  spindle. 

3.  Non-rotating  parts. 

4.  Large  turbine. 

5.  Disregards  direction  of  filaments. 

(1)  The  bearings   of  a  turbine   are   subjected  to    an  end  thrust 
due  to  the  weight   of  the   turbine,    and  to   a   side  thrust   due   to  the 
force   of  the  water  against   the   turbine.     These   forces,    after  a  time, 
begin  to  wear  the  bearings  quite   appreciably,   and   it    is    then  that 

the   rating  is   affected.     The   condition  of  the  bearings   does   not   seem 
to  affect  the  middle   portion  of  the   rating   curve,  but  the   starting 
velocity   curve    is   always   lengthened  while  the   slope   of  the  upper 
section  of   the   higher  velocity   curve   is  usually  altered. 

(2)  The   point  bearing  at  the   end   of  the  spindle  about 
which  is  keyed  a  turbine   of  relatively  large  diameter  gives   rise 

to  another   source   of   trouble.     Any  accidental  blow,   even  if  of  small 
magnitude,   delivered  to   the   rim  of  the  turbine   is  multiplied  by  the 
2.5   in.,    or  more,    lever  arm,   and  the   resulting  moment   is  almost 
certain  to  bend  the  spindle,    or   else  break  the  point.      In  sup- 
port  of   the   last   statement,   Mr.   Hoff  says:    "ishall   venture  to  say 
that  50   per   cent   of  the  meters  which  are   sent  into   this   office 
for   repairs  have   broken  points".     An  operator  does   not  know  when 
the   shaft  becomes   bent,   and   consequently  does   not   know  when  the 
gaging  data  begins  to  be  worthless,   because   any  misalignment   of  the 
shaft   or  broken  point   is   always   accompanied  by  an  increase   in  the 

instrumental   friction  and  a  resultant  alteration  of  the    rating 
curve . 


60 


(3)  All  of  the  turbine  meters   have   a  number  of  non- ro- 
tating parts.     Any  change    in  the   direction  of  the    stream  filaments 
alters  the  eddy  currents   formed,   as   shown  before.     The  yoke,    in 
which  all  turbines   are   suspended,    is   a  very  bad   feature,  because 
of  its   proximity  to  the  turbine   itself.     The   Price  meter  rotation 
is    increased  10  per  cent  when  the  yoke   is   placed  up-stream.      Con- 
sequently,  any  change   in  direction  of  the   stream  lines   produces 

a  proportional   change   in  the   rotation,  which  is    certainly  not  to 
be  desired. 

(4)  A  turbine   5   in.   in  diameter  could  not   be  expected 
to  show  accurate   results    in  a  small   irrigation  ditch  because   of  the 
widely  felt  disturbances   produced  at  these   lower  velocities   around 
even  a   small   obstacle.     The  velocities   immediately  at  the   sides 
and  bottom  cannot  be  determined  at   all. 

(5)  Any  meter  which  rotates   at   practically  the   same   speed 
regardless   of  the   direction  of    stream  filaments  has   no  place   in  the 
field  where   parallel  filaments   are   never  encountered.      In  reply  to 

a  question  regarding  the   accuracy  of  one   of  the   standard  makes   of 
turbine  meter,   a  prominent  engineer  said:    "You  can  never  tell — any- 
whers   from  5  to  25  per  cent.      It's   not  much  better  than  a  guess". 
The  writer  believes   that  the   inaccuracies   of  a  turbine  meter  are 
largely  due  to  this    inherent  disadvantage. 

In  normal   position,   the   Price  meter   rotates  at   42  to  44 
revolutions   per   100  ft.     With  th«  yoke  up-stream,  the   rotation  is 
increased   10  per   cent.      No  test  was  made  to  determine  the   variations 
in  rotation  between  these  two  positions,  but   it   can  be   seen  that  due 
to  the  design  of  the   turbine   itself,   not  even  an  approximation  to 


61 


1 
the   cosine   law     can  be   expected. 

The   Price  meter  as   a  horizontal   shaft  meter  was   discussed 
in  Section  17.     Here,   an  average   of   the   starting  velocity  curves 
shows  that   for  low  velocities  the  meter  rotates  about  33   revolutions 
per   100   ft. --about  23  per  cent   less   than  when  in  normal  position. 
A  meter  to  be   successfully  employed   in  the   integration  method   of 
gaging  must   not   rotate  when  moved  up  or  down.      If  the   vertical 
motion  is    reduced  to,    say,   0.02   ft.   per  second,   probably  no  rota- 
tion would   occur,  but  the  tendency  to  turn  would   still  exist,   ard  the 
results  would  be   affected  accordingly. 

22.     Advantages   of  the  Hoff  Horizontal  Shaft  Propeller 
Type  Meter. — 

1.  Strong,  well  built,    simple,    fool-proof. 

2.  Negligible   friction  factor. 

3.  Short   starting  velocity  curve. 

4.  Few  non-rotating  parts. 

5.  Small   rubber  propeller. 

6.  Adaptable  to  high  as  well   as    low  velocities. 

7.  Approximation  to   cosine   law. 

(1)     All   of  the  metal  parts   of  the   Hoff  meter  are  made   of 
non-corrosive  material,   and   each  part   is  designed  so  as   to  be   of  the 
least   possible   size,   and  yet  be   strong  and  durable.      Simplicity  has 
been  one    of  the  designer's   aims,   and  he  has   succeeded  well.     The 
most   complex  part   of  the   instrument   is   the   counting  device,   but 
by  removing  one   screw  and   lifting   off  the   cover  plate,    one   can  see 
that   a  simpler  mechanism  could  not   have  been  designed.     This   is 


Ses   Section  22. 


I    -- 

.*    -H 


O 
f\l 


u> 

•H 


I-  O 


63 


shown  in  Fig.  16.  There  is  nothing  to  get  out  of  repair.   If  the 
contacts  neod  an  adjustment,  the  points  are  tightened  or  loosened, 
as  the  case  may  demand;  if  the  plate  is  removed  beforehand,  this 
adjustment  can  be  mado  more  quickly  and  accurately,  since  the  opera- 
tor can  see  just  what  he  is  doing. 

(2)  This  meter  is  characterized  by  a  very  small  friction 
factor,  as  can  be  seen  from  the  rating  curves  in  Figs.  13,  14  and  19. 
This  advantage  has  been  gained  by  the  employment  of  an  ingenious  set 
of  bearings.  The  end  thrust  is  absorbed  by  a  jewel  bearing  in  the 
rear  socket.  The  shaft  bearing — that  bearing  which  carries  the 
weight  of  the  spindle  and  propeller — is  simply  a  guide  ring  into 
which  the  shaft  fits  rather  loosely.   By  making  this  bearing  loose- 
ly fitting,  any  additional  looseness  caused  by  wear  is  not  likely 

to  affect  the  rating.  The  propeller  is  very  small,  being  only  4 
in.  in  diameter.  A  drawing  of  the  propeller  to  full  scale  is  shown 
in  Fig.  20.   Its  weight  is  materially  reduced  by  making  it  of  hard 
rubber  the  specific  gravity  of  which  is  1.2.  Besides  reducing  the 
friction  factor,  a  rubber  propeller  has  the  advantage  of  being  able 
to  withstand  a  great  deal  of  abuse  without  any  danger  of  changing 
its  pitch. 

(3)  Reducing  the  friction  factor  is  naturally  productive 
of  a  shortening  in  the  starting  velocity  curve.  The  starting  veloci- 
ty curve  of  all  of  the  Hoff  meters  terminates  at  approximately  1  ft. 
per  second.  This  is  quite  an  advantage  over  the  turbine  type  of 
meter,  because  with  this  type  the  starting  velocity  curve  invariably 
extends  to  2  or  2.25  ft.  per  second.   Since  the  reliability  of  ob- 
servations made  within  the  zone  of  the  starting  velocity  is  to 

be  questioned,  this  meter  is  particularly  well  adapted  for  irri- 


1J8VJ 


oee 


64 


gation  investigations. 

(4)  The  Hoff  meter  is   not  burdened  with  any  unnecessary 
non-rotating  parts.      It   has   no  yoke;    it  has   neither  protecting  wires 
nor   rods   for   the   propeller.     The    simplicity   of  design  has  eliminated 
all   these   dispensable   parts  which   are   usually  found   in  the   construc- 
tion of  a  current  meter.     This   meter  causes   less  disturbance   in  the 
stream  flow,   and   less  eddies   are   produced.      Consequently  more   accu- 
rate  results   should  be   obtainable  with  its   use. 

(5)  Another  point   in  favor  of  the  meter   is   its   small  pro- 
peller,  this   meaning,    of    course,   that  the   rotating  part   itself  will 
cause   less  disturbance   in  the   flowing  filaments.      The   small  propel- 
ler  is  especially  advantageous   in  gaging  -very  small   channels  be- 
cause  observations   can  be   made  nearer  the   side  walls   and  bottom. 

(6)  The  Hoff  meter  rotates   from  78  to  80  revolutions 
per   100  ft.     With  only  a  1  to  1   counting  device,    it  would  be   quite 
difficult  to  accurately  record  the  higher  velocities.     This   instru- 
ment,  as  described  before,   has  two  counting  devices:   the  5  to  1 
ratio  used  for  the   higher  velocities,    and  the   1  to  1   ratio  used   for 
the    lower  velocities.     This   makes  the  meter  equally  well  adaptable 
to  both  high  and   low  velocities. 

(7)  Suppose   a  horizontal   shaft  meter   is    lowered   into  a 
stream  so  that   its   axis   is   parallel  to  the   stream  filaments,   and  the 
propeller   rotates   at  the   rate   of  0.5   revolutions   per   second.      Now 
turn  the  meter  about  the   supporting  rod  as   an  axis   so  that   the  cen- 
ter line   of  the   shaft  makes  an  angle  tf  of,   say,    60     with  the   stream 
filaments.     The  meter  should  now  rotate   at   0.5  X  Cos   60     or  0.25 
revolutions   per  second.      In  other  words,   the  discharge   of  a  stream, 


65 


Q  -  av 

where  a  is   the   cross   sectional   area  of  the   stream,   end  v  is    the  veloci- 
ty of  the   stream  perpendicular  to  the   plane   of  area  ji.     Thus,    if  the 
base   plane   in  which  the   gaging  is  being  done   is   not  taken  perpen- 
dicular to  the   stream  (assuming  for  the  moment  that  parallel   fila- 
ments  do  exist),   but  makes   an  angle   (90  -   $}  with  the    stream,  the 
discharge, 

Q  »  a'v  Cos  $ 
where   a1    is  the   new  crosn   sectional  area. 

If  a  meter  can  be  designed  which,  when  held  perpendicular 
to  the   above  base   plane,  will   indicate   a  velocity  of  TT  Cos  j6  in- 
stead  of  v,   the  designer  will  have  made  another  long  stride  toward 
the   ideal.     A  meter   fulfilling  this    requirement   is  said   to  follow 
the   cosine   law.      Obviously,   it   can  only  be   a  propeller  type  meter, 
the  propaller  having  flat  face*. 

A  met.ev  whi^h  follows  the   cosine   law  will   accurately  gage 
any  stream  regardless   of  the  direction  of  the   filaments.      It  will 
indicate    only  that   component   of  velocity  which  is  perpendicular 
to  the  base   plane,   provided  the   instrument  is   rigidly  supported, 
and  the   angle  between  the  base   plane   and  the   propeller  axis   is  90   . 
When  $  =  90   ,  the   rotation  should  be   zero.      Consequently,    a  meter 
of  this   type  would  be   particularly  well  adapted  to  the   integration 
method   of   gaging,  because   any  vertical  movement  would  not   tend  to 
rotate   the   propeller. 

A  test   of  the  Hoff  meter  with  various  values   of  the   angle 
0  shows   that  this   instrument   is   not   far  from  the   ideal   in  this 
respect.     Tables   10  and   11   show  the  data  obtained.      If  the  meter 
were   rotated  about  the   supporting  rod  as   an  axis   in  a  clockwise 


, 


. 

Tftfc     * 


66 


S  a; 


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O    3     <U 
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re    oj 

£8.8 

•p*    -H    t-1 

cc  >  o 


67 


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a    cs    to 

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a 

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68 


Theoretical  Curve 

,Vith       Arbitrary 

Correction  Applied 


THEORETICAL  AND  EXPERIMENTAL 
•COHVES  SHOWING! 

:  VELOCITIES  AS    -ORBilSATES- 

AGAINST ;  VALUES  OF     0  AS  '/iBBG IS<>AS . 


Fig.   23, 


69 


Table   10. 


Table   11. 


Rating  of  Hoff  Meter,  Model  21,   No.   48.      Jan.   25,    1922. 


'.Then  j6  is  positive. 

Time      in     Revo-  Revolutions     Ft.   per 

seconds,      lutions.      per  second,      second. 


Course:   200  ft. 

0° 

101.7 

157 

1.54 

1.97 

0° 

287.8 

153 

.532 

.695 

10° 

176.2 

146 

.828 

1.14 

10° 

216 

149 

.69 

.926 

10° 

196.4 

149 

.759 

1.02 

Course:   51.5 

ft. 

0° 

21.8 

41 

1.88 

2.36 

0 

40.5 

40.7 

1.005 

1.27 

°o 

68.8 

41V 

.596 

.748 

50 

22 

40 

1.82 

2.34 

f.0 

39.5 

39.9 

1.01 

1.3 

62.7 

39.2 

.625 

.823 

10o 

40 

38.2 

.955 

1.29 

10o 

65.2 

37 

.569 

.791 

10o 

21.8 

39 

1.79 

2.36 

15o 

22 

37.3 

1.69 

2.34 

15o 

41.2 

37.2 

.904 

1.25 

15o 

64 

36.6 

.572 

.805 

20o 

24.2 

34 

1.4 

2.12 

20c 

41.8 

32.5 

.777 

1.23 

20o 

52.4 

33 

.63 

.983 

30o 

23.7 

26 

1.1 

2.17 

30o 

24.2 

27 

1.12 

2.13 

30c 

41.9 

26.2 

.625 

1.22 

40o 

24 

18 

.75 

2.14 

40o 

41.6 

17.9 

.43 

1.23 

40Q 

60.8 

16.8 

.276 

.846 

4^o 

21.7 

12.6 

.58 

2.37 

45o 

40.6 

12.4 

.307 

1.27 

0 

61.8 

11.8 

.191 

.834 

50  0 

21.1 

8.1 

.382 

2.43 

50  0 

39.8 

7.5 

.189 

1.3 

500 

62 

6.2 

.103 

.83 

550 

22 

4.2 

.191 

2.34 

550 

40.5 

3.2 

.079 

1.27 

550 

60.2 

2.2 

.037 

.856 

600 

No  rotation. 

650 

n          n 

700 

n          it 

750 

it          u 

80C 

21.8 

-5.5 

-.252 

2.36 

850 

21.8 

-9.1 

-.417 

2.36 

80 

21.8 

-10.5 

-.482 

2.36 

iVhen  $  is  negative. 

Time      in     Revo-  Revolutions      Ft.   per 

seconds,      lutions.      per  second,      second. 


41.7 

64.9 

22 

40.2 

65 

22 

41 

65.2 

21.8 

4C.9 

63.7 

21.8 

41.8 

62.5 

21.9 

39.9 

62.6 

22 

39.6 

63.5 

22.3 

40 

60.7 

22 

39.7 


39.9 

39.8 

39.5 

39 

37 

33.8 

36.8 

35.1 

33.5 

33.8 

30.6 

29.7 

26.3 

25 

23.3 

16 

15.1 

13.7 

11.9 

10.8 

8.7 

8. 

7.2 

6.05 

4. 

2.3 


No  rotation. 


it 
it 


1.81 
.953 
.609 

1.77 
.92 
.52 

1.67 
.856 
.514 

1.55 
.748 
.475 

1.21 
.598 
.373 
.73 
.378 
.219 
.  41 
.273 
.137 
.359 
.18 
.0997 
.182 
.058 


2.34 
1.24 

.794 
2.34 
1.28 

.793 
2.34 
1.26 

.791 
2.36 
1.26 

.808 
2.36 
1.23 

.823 
2.35 
1.29 

.823 
2.34 
1.3 

.811 

?     •Z 

w  •  W 

1.29 

.849 
2.34 
1.3 


21.7 
21.8 
22 


-5.5 
-9. 
-10.8 


-.253 

-.413 

-.491 


2.37 
2.36 
2.34 


70 


direction,   $  was  marked  plus;    in  a  counter-clockwise  direction, 
minus.     The   corresponding  curves   are   plotted   in  Figs .   21  and  22. 

In  Fig.   23,   ft.   per   second   are   plotted  as   ordinates 
against  $  as   abscissas,  where   the   normal  velocity  was   1.5  ft.   per 
second.     The  dsta  for  this    curve,  marked   "test   curve"   is  taken  from 
Figs.   21  and  22,   at  the   velocity  of   1.5   ft.   per  second,   and   listed 
in  Table   12,    columns    (2)   and   (3).     The   average   of  the   positive   and 
negative  values,    column  (4),   are  the   ones   plotted.     The   ideal 


Table  12. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

Revolutions 

Revolutions 

per  second 

per  second 

Average 

for  positive 

for  negative 

revolutions 

Ft.  per 

Cos  $  X  1.5  ft. 

0 

values  of  $ 

values  of  $ 

per  second 

second 

per  second 

0 

1.58 

1.58 

1.58 

1.5 

1.5 

5 

1.56 

1.54 

1.55 

1.47 

1.49 

10 

1.51 

1.48 

1.5 

1.42 

1.48 

15 

1.44 

1.39 

1.42 

1.35 

1.45 

20 

1.32 

1.26 

1.29 

1.22 

1.41 

30 

1.03 

1.01 

1.02 

.965 

1.3 

40 

.7 

.61 

.66 

.625 

1.15 

45 

.49 

.44 

.47 

.445 

1.06 

50 

.29 

.31 

.3 

.285 

.964 

55 

.13 

.14 

.13 

.123 

.86 

60 

.75 

65 

.635 

70 

.513 

75 

.389 

80 

-.21 

-.21 

-.21 

-.199 

.261 

85 

-.35 

-.35 

-.35 

-.332 

.13 

90 

-.42 

-.42 

-.42 

-.399 

0 

curve  is  marked  "cosine  $" .  The  values,  1.5  ft.  per  second  X  Cos  0, 
are  shown  in  column  (6).  There  is  an  appreciable  difference  between 
the  ideal  curve  and  the  test  curve.  Still,  the  Hoff  meter  is  the 

only   one  which  even  approximates  the   ideal,   and  this   is   certainly 

o 
another  point   in  its   favor.     V,rhen  jp  »  90   ,  the   rotation  is   negative, 


71 


(o) 


uatlo 


. 

-•   an  end   sect:  a  Hoff  iler 


V'in.st    '  •?« 

Lve  faces  A,  •  ,  no  force 

. 

•n  for   this    r- 


72 


resentation  will  be  disclosed  later.  Face  A_  makes  an  angle  a  with 
a  line  perpendicular  to  the  center  line  of  the  propeller  shaft;  B, 
an  angle  b;  C,  an  angle  c. 

Fig.   24   (b)    shows  a  filament  acting  against  the   front 
face,  A.     What  torque   component  does  this    filament  exert? 

Let  dF   »  the   force   due  to  impact   of  the   filament. 

Then,   dF  makes   an  angle    (90  -  a)  with  the   face  A. 
Upon  striking  the   face,   dF  is   resolved  into  two  components:   ds, 
the   slippage    component   parallel  to  A,   and  de,   the  effective   com- 
ponent perpendicular  to  A.     de   is  then  resolved   into  two  components: 
dt,   the  thrust   component   parallel  to  the   spindle,   and  dq,   the  torque 
component  perpendicular  to  the   spindle. 

de    -  dF  Cos   a 

dq   =  de   Sin  & 

• 

.    .     dq   «  dF  Cos   a  Sin  a 

where   dq  is  the   component  causing  rotation. 

Suppose,   however,   that  the  filament  is   not   parallel  to  the 
spindle,  but  makes   an  angle   0  with  it,   as    in  Fig.   24   (c).     Then, 
what   is  dq  in  terms   of  a  and  j6l 

de   -  dF1   Cos   (a  +  0) 

dq  =  de  Sin  a 
• 
.  .  dq  »  dF1  Cos  (a  +  $)  Sin  a 


Let  •&•  »  angle  of  displacement  from  the  position 

o 
shown,  where  -6-  =  )  . 

In  other  words,  when  the  propeller  has  revolved  one-fourth  revolu- 
tion, -6-  =  90°;  one-half  revolution,  -6-=  180°;  etc.  \7ith  the  fila- 
ment approaching  the  propeller  at  the  angle  $,  what  is  the  torque 


pJb   sieriw 


73 


component  when  •$•  =  90°? 


At  -9-  =  180° 


At  -6-  =  270° 


dq     Q   0   »  dF1    Cos   a  Sin  a  Cos   j6 

A      «7W 


180° 


dq  2  o  =  dF1  Cos  a  Sin  a  Cos  fi 
At  -6-  -  360°,  or  0° 

dq   0  =  dF1  Cos  (a  +  $)  Sin  a 

In  other  words,  the  torque   component  varies   from  a  minimum  at  •&--  0° 
to  a  maximum  at  -d-  *  180   ,   and  back  to  a  minimum  at  •£•  =  360   ,    or  0°, 
the   curve   being  two  straight   lines. 

If  the   face  A  were  the   only  one  active,  the   propeller 
would  theoretically  follow   the   cosine   law;   but  this  is   not  the   case. 
When  0  reaches   25   ,   face   B,   at  -9-  =  0°,    is   parallel  to  the   filament, 
and  any  further   increase   in  $  brings   B  into  play.      In  a  like  manner, 
when  $  reaches  40   ,   face  £,   at  -9-  *  0   ,    is   parallel  to  the   filament, 
and  any  further   increase   in  $  brings   C   into  play.      So,   it    is   necessary 
that   each  face  be   considered   separately. 

Disregard  the  existence   of  face  A  for  the   present,  and 
assume   that   the   filaments   impinge  upon  faces  ]3  and  £,   as   shewn. 
An  analysis   of  the  way  in  which  the   force   dF*    is   resolved  gives 
t.  e   following  equations    similar  to  the  previous   ones: 
dq0  no  =  dF1    Cos    (b   +  f}   Sin  b 

O     V 

dq    0  -  dF1  Cos  b  Sin  b  Cos  j6 
B  90 

dq     o  z  dF'  Cos  (b  -  $)  Sin  b 
B  180 

dq     0  =  dF1  Cos  b  Sin  b  Cos 

B 


dclr.  no   =  dF1    Cos    (c   +  $)   Sin  c 

v     U 

dq          o   *  dFf    Cos    c  Sin  c   Cos 

c  yo 


Tt 

."o   »rio 
<  '     ari 

, 


x   anb-toi 


77 


T> 

tO  tO  to                LO          LO          CO   CO 

.. 

^  CO  to         *d*  CO          CO   ^   to   to 

o 

0 

tOC^CO         O>O>          O^OSCOD^ 

fj 

o 

.  x 

I  —  1 

OO 

ir 

I  —  1 

SP 

0 
O 

i 

II 

S-O 

(-», 

^ 

ooo        ooooooc 

0   0 

"l 

ooo      ooooooo 

CM   10 

C! 

tO   T}<   tO          CM   i  —  1          rH  CM    tO   ^J! 

—  ^ 

1      1      1      1 

r     II 

pj 

0     0 

•rH  •  ' 
-P 

o 

5 

o 

to       CM       to       to  CM        to  to 

tOlOtO           rH           rHtOtOtOC- 

rt 

rH 

o 

»J 

O     1      1      1      1      I 

3 

n 

C 

O 

1     1 

™ 

u 

a! 

,- 

O 

a. 

ooo        ooooooo 

000         OOOOOOO 

o 

rH   rH   rH    rH   rH 

•  • 

i 

to^c-toa>totototototo 

,0 

o 

&2   t**   O    ^O    i    !    O    JO    O>    vJJ    *£J    O 

o 

—  -* 

^    LO    C*-    C—    CO    Oi    O*    OS     Oi    U  *    QJ 

c 

CO 

r, 

rH 

r-H 

0 

V 

II 

a 

ni 

—  -. 

• 

(^ 

ki 

OOOOOOOOOOO 

to 

S-*O 

i 

LO    LO    LO    O    LO    LO    LO    LO    LO    LO    LO 

r-H 

O   id 

Q 

CO    LO    ^*    ^    tO   CXJ    i—  1               1     c—  4   OJ 

^H    CO 

_^ 

1    1 

C' 

n     II 

,5. 

C 

0    ,0 

Q 

tooit-       c-cnto^<c-a>co 

C—  1 

•rH    

H- 

EJJ           ?R           ^"^           Lu     rt    ^^    Iv^    r^ 

^J 

O 

o 

^*  CVi    O           C)  C^     ^*    LO    C*-    CO    O* 

•3 

o 

1 

R 

O 

O     1     1     1      1      1     1     1 

0 

CJ> 

rH 

<f> 

O 

•f 

ooooooooooo 

LO    LO    LO    C3    tO    LO    LO    LO    LO    LO    LO 

'^, 

CO    ^^    OO    Oi    O5    C5    f~~^   C\J    tO    ^^    LO 
i-i    r-t    <-H    »H    i-!    f-l 

•7 

CO   CO    CO                   LO            LO            CO    CO 
^   CO  CO          *vj*   CO           00    ^*    CO   CO 

ii 

o 

c: 

co  ^-  oo       *j~>  o^        O5  0^  oo  t— 

o 

0 

CO 

r/ 

r-i 

rH 

rH 

O 

to 

O 

s 

n 

4 

,  —  ^ 

(j) 

r^i 

ooo        ooooooo 

^Q 

| 

ooo      ooooooo 

o  o 

t 

LO    ^    tO           CVl    rH           rH   CM    tO   ^ 

CM   m 

tiii 

n    n 

0     OS 

B_J   ^  ^ 

t7 

tO          CM           tO          tO   CM           tO    CO 

49 

o 

o 

ri 

«j<          ^           t~          t-   ^           •'i1    to 
(OUJtO            rH           rHtOLOtOC- 

•a 

II 

V. 

O     1      1      1      1      I 

0 
rH 

I 

0 

o 

f7 

ooo        ooooooo 

+ 

ooo      ooooooo 

ci 

lO   to  t*-          CO   O^   O   i  —  1  CM    CO   ^t* 

rH   rH   rH    rH    rH 

OO      OOOOOOOOO 
OOOiOOOOOOOO 


I      I 


78 


180° 

dq  o   =  dF1    Cos   c  Sin  c   Cos  $ 

C   £  I U 

A  glance  at   Figs.   25,   26  and   27  will  make   the   problem  clearer.      In 
Fig.   25,   the   function  of  the  torque   component  for  the   face  A  is 
plotted   for  values   of  $  from  0     to  90    .     These  values   are   plotted 
for   only  one-half  revolution  of  the   propeller  because  the   curves 
are   identical   for  the  two  halves.     Also,   the    curves  were    located 
by  plotting  only  the  values   at  -Q-  =  0   ,    and  •$•  =  180°,  because  they 
are   all   straight   lines.      In  Fig.   26,   similar  curves   for  face   B  are 
plotted;    in  Fig.   27,    for  face  £. 

Referring  to  Fig.   25,  what  do  the   negative   components 
mean?     Take  $  »  50   ,   for  an  example.     From -&-    =  0°  to  -0-    «  16°, 
face  A  is   not   exposed  to  the    approaching  stream;    it   is   hidden  behind 
the   face  B.     These  components  which  are   negative,    in  this  case,  are 
not  active . 

In  Fig.   26,   the   curves  are  somewhat  different.     Here,   the 
positive   components   indicate   nothing;  where  the   curves   show  positive 
values,   the  blade   B  is    inactive.     The   negative    components   indicate 
that  the   face   B   is  exposed  to  the   oncoming  filaments,    and  that  this 
torque  tends  to  reverse   the   rotation. 

Fig.   27  presents   a  still  different  situation.     Here   again, 
the   negative    components  mean  nothing;    face  C   is   hidden  by  faces  A 
and  B.     When  the    components   are   positive,   the   face    C   is   exposed  to 
the   oncoming  filaments,   and  the   resultant  torque  tends   to  turn  the 
propeller   in  the   normal  direction;    it  assists   the  torque  exerted 
on  face  A. 

This   analysis   is   a  difficult   one   to  make   clear  to  the 
reader,  because   it   is  a  three  dimensional   problem.     Possibly  Ta- 


Table   14. 


79 


(1) 

Average  value   of 
a  ct  i  ve   c  omp  one  nt 
from  curve   for 
face- 
A              B                C 
(2)          (3)             (4) 

H 

•H 

X! 

CM 

(5) 

X! 

£> 

c 

•H 

X! 

V~N 

to 

(6) 

o 

X! 
0 

fl 

•H 

X! 

**"N 

CT) 

Total  theoretical 

CD 

^torque  component  X  K 

* 

3-1          LO  1 
0         r-t  \ 

e>       -tf 
§        g 

T(           O 
4)           tf) 

K         « 

(9) 

0° 
10° 

.643 
.633 

.444 
.437 

.444 
.437 

1.5 
1.477 

20° 

.605 

.418 

.418 

1.413 

25° 

.583 

0 

.408 

0 

.403 

1.363 

30° 

.557 

-.043 

.385 

-.039 

.346 

1.17 

40° 

.494 

-.129 

0 

.341 

-.117 

0 

.224 

.756 

50° 

.5 

-.212 

.087 

.345 

-.192 

.02 

.173 

.584 

60° 

.492 

-.287 

.171 

.339 

-.26 

.039 

.118 

.399 

70° 

.47 

-.353 

.25 

.324 

-.321 

.057 

.06 

.203 

80° 

.433 

-.409 

.322 

.299 

-.371 

.074 

.002 

.007 

90° 

.383 

-.453 

.383 

.264 

-.411 

.088 

-.059 

.-.199 

80 


bles  13  and  14  will  be  of  some  benefit. 

Table  13  ^hows  the  calculations  from  which  the  curves  in 
Figs.  25,  26  and  27  were  plotted.  Table  14  shows  the  average 
torque  components  as  taken  from  these  curves.  The  average  torque 
exerted  on  face  A  for  one  revolution  for  a   particular  value  of 
$  is  proportional  to  the  mean  ordinate  of  that  portion  of  the  curve 
corresponding  to  that  particular  value  of  $  above  the  X-axis. 
These  are  positive  components;  the  values  are  tabulated  in  column 
(2).   The  average  torque  exerted  on  face  B  for  one  revolution  for 
a  particular  value  of  $  is  proportional  to  the  mean  ordinate  of 
that  portion  of  the  curve  corresponding  to  that  particular  value 
of  $  below  the  X-axis.  These  are  negative  components;  the  values 
are  tabulated  in  column  (3).  The  average  torque  exerted  on  face 
C  for  one  revolution  for  a  particular  value  of  $  is  proportional 
to  the  mean  ordinate  of  that  portion  of  the  curve  corresponding  to 
that  particular  value  of  j6  above  the  X-axis.  These  are  positive 
components;  the  values  are  tabulated  in  column  (4). 

Since  the  height  of  the  blade  is  the  same  for  all  faces, 
and  since  the  three  faces  appear  in  each  of  the  four  blades,  the 
torque  on  any  face  for  the  four  blades  is  proportional  to  the 
values  taken  from  the- curve  multiplied  by  the  width  of  the  face. 
Let  w  =  width  of  face  in  in. 
Then,  w  =0.9 

A 

w   =  1.0 
B 

w   =  0.3 
C 

.  .  the  total  torque  on  the  face  A  for  the  four  blades 

TA  =  k  X  M  X  w 

A        A    A 

where  k  is  a  constant  including  the  length  of  the  blade,  the  number 


81 


of  blades,   the   friction  factor,   adhesion,    and   any  other  factors  which 
tend  to   oppose  the   rotation  of  the   propeller;   M     is   the  mean  value 

A 

of  the  torque   function  taken  from  the   curve . 

On  the   face   B,   T      =  k  X  M     X  w 
-       B  B          B 

On  the   face   C,   T      =  k  X  M     X  w 

~~     c  c       c 

Values   for  M.    are   shown  in  column  (2);   for  K  ,    in  column 
A  B 

(3);    for  Mp,   in  column  (4).     Values   for  T.    are    shown  in  column  (5); 
for  Tg,    in  column  (6);   for   T.,   in  column   (7). 

T      +  T      +  T      =  total  theoretical  torque  X  K 

ABC 

and  the  values  are   shown  in  column  (8).     These  values   are   reduced 

to  ft.   per   second  by  multiplying  them  by  the   constant   1.500;   this 

0.444 

does   not   change  the  normal  velocity  of  1.5   ft.   per  second,   con- 
sequently,  the   resultant   curve    is   comparable  with  the  test   curve 
shown  in  Fig.   23. 

Referring  to  Fig.   23  again,    it  will  be   noted  that   the 

curve   just  developed,  marked   "theoretical  curve   as   developed", 

.  o 

crosses  the  X-axis  when  0  is   about  80    .     The  test  curve    shows   that 

the   propeller  does   not    rotate  between  $  -  60     and  $  =  75   ,   and 
beyond  the   latter  value   of  $  the   rotation  is    negative. 

Much  to  the  writer's   disappointment,  the   two  curves   show 
little   similarity.     The   theoretical   curve  shows  two  decided  breaks. 
At   $  *  25     the   curve  begins  to  fall   rapidly  due   to  the   retarding 
influence    of  the   face  Bj    at  $  =  40   ,  the   slope   is  decreased 
slightly  due   to  the  propelling  influence   of  the   face   C.     A  decided 
break,   such  as   these   are,  would   naturally  not  appear   in  the   test 
curve,  though  it    seams   that  a  slight  depression  might  be  expected. 

If  an  arbitrary  constant   is   applied  to  the   theoretical 
curve  so  that   it  will   also  cro-?*  the  X-axis   at   $  =  60   ,   a  resultant 


82 


curve,  marked  "theoretical   curve  with  arbitrary  correction  applied", 
is    obtained. 

In  attempting  to  apply  a  standard  equation  to  the   test 

curve,    it  was   found  that  Cos   3  j6  fits   the   positive  values  very 

~Z~ 

closely.      It  appears  to  the  writer  to  be   nothing  more  than  a  co- 
incidence,  though  there  may  be    some   reason  for   it. 

It  might  be   said   here  that  a  development   of   the  torque 
exerted   on  a  very  thin  blade   having  only  two  flat,   parallel   sides, 
or   on  a  blade  whose   cross   section  is  a  closed  triangle  will   result 
in  a  cosine   curve.     '.Vhether   or  not  a  meter  with  this  type   of  pro- 
peller would  actually  give   a  cosine    curve,    or  even  a  close   approxi- 
mation could   only  be  determined  by  experiment. 

24.      Disadvantages    of  the   Hoff  Horizontal  Shaft   Propeller 
Type  Meter .--Compared  with  other  current  meters,   the  Hoff  instrument 
has   no  disadvantage.     The   rating   curve   always   lies   below  the   ideal 
curve    on  account   of  the   small   interference  factor.     This   may  appear 
to  some  as   a  disadvantage,   though  the  writer  believes  that  this    type 
of  curve--a  straight   line   slightly  below  the   ideal  curve — is    ju-rt 
as  well. 

Of  course  the   Hoff  meter   is   not   perfect.     Ag  was   stated 
in  the  beginning,   a  perfect  meter  cannot  be   made.     This   meter  offers 
small   interference  to  the   stream  filaments;    it   possesses   a  small  a- 
mount   of  friction;    it  does   not  exactly  follow  the    cosine   law.     The 
first  two   objections   cannot  be  eliminated.     Whether  or   not  the  third 
objection  can  be   overcome,   the  writer   cannot   say;   but  the   Hoff  curve 
approaches   the  .copine   curve,    and  this    can  be   said   of  no  other  meter. 
So,   taking  all  factors    into   account,   and    considering  both  the   con- 
clusions drawn  from  the  theoretical  analysis   and  the  actual  tests, 
the  writer  believes   that  the  Hoff   instrument   is   nearer  the   ideal 


83 


than  any  other  raster  which  has  yet,  been  made. 

V.      CONCLUSIONS, 

25.      Conclusions .--In  conclusion,    it   might  be  well  to  re- 
view the  most   important  points   as   set   forth  in  this  thesis. 

1.  The   current  meter  method   of  measuring  stream  flow 
.fill   never  produce  accurate   results,   because  when  any  obstacle, 
suce  as   a  currant  meter   is,    is  placed   in  a  moving  stream,   a  cer- 
tain retardation  of  the   fluid   is  effected,   and  eddy  currents   and 
cross   currents   are   produced  from  the   non-parallel   filaments  which 
introduces  errors   of  uncertain  magnitude . 

2.  The  vacuous   spaces   formed  behind  any  obstacle  material- 
ly affect     the   force   required  to  hold  that   obstacle   in  the  moving 
stream.      It   is  to  this    phenomena  that  the  turbine  meter  is   largely 
responsible   for   its   rotation. 

3.  A  disturbance   is  more  widely  felt  when  the  velocities 
are   low,  while  the  height  to  which  the  water   is  piled   in  front   of 
an  obstacle   and  the  depth  to  which   it  falls   in  the   rear  is   greater 
when  the  velocities   are  high.     This  makes   the   accurate   gaging  of 
small   channels  very  difficult,   because   the    stream  filaments   are 
deranged  throughout   the  entire   cross   section  of  the   ditch  when   a 
meter   is   lowered   into   it. 

4.  The   slops   of  a  rating  curve  depends   not   only  upon 
the   characteristics   of  the   rotating  element   itself,   but  also   upon 
the   interference   offered  by  all   of  the   non-rotating  parts:   the 
supporting  rod    or  cable,   tail,   yoke,   any  protecting  devices   for  the 
propeller   or  turbine,   etc.     The   interference   factor   of  the   propeller 
or  turbine   causes  the   higher  velocity  curve  to   lie   below  the    ideal 


84 


curve.     The   instrumental  friction  factor  gives   the   starting  veloci- 
.ty  curve   a  steeper  slope  than  that    of   the   higher  velocity  curve,   and, 
on  this   account,   the  two   curves   intersect   at   a  point  below  which  the 
observations   cease   to  be   reliable. 

5.     All   current  meters   have    their  advantages   and  disad- 
vantages.    By  a  careful   study  of  the   nature   of  fluid   flow  around 
obstacles,   and  close   attention  to  the  minute  details,  the  designer 
can  eliminate   many  of  the  disadvantages,    and   improve  those  which 
are    indispensable.     The   horizontal   shaft  propeller  meter   is    correct 
in  principle.      Its   precision  cannot  be  excelled  by  any  other  type. 


85 


Bibliography. 

Bateau,   M. : 

"Experiments   and  Theory  on  the   Pitot  Tube   and   on  the   Current 
Meter   of  ifoltmann."      (Annales  de  Mines  Memoires,  Vol.    18,    1898, 
and   10th  series,  Vol.   2,    1902.)      (Manuscript    in  the   Office   of 
Irrigation  Investigations,   Berkeley,   California.) 

Ccwley  and  Levy: 

"Aeronautics    in  Theory  and  Experiment". 

de  Villamil,  R. : 

otion  of  Liquids". 

Epper,  M. :  1 

Hydrometric  Experiments  . 

Foote,  A.  D.: 

">7ater  Meter   for   Irrigation  (A)".      (Trans.  A.S.C.E.,  Vol.   XVI, 
1887.) 

Groat,   8.   F.: 

"Characteristics   of  Cup  and  Screw  Current  Meters".      (Trans. 
A.S.C.E.,   Vol.    LXXVI,    1913.) 

"Current  Meters".      (Part  V,    "Cheni-Kydroinetry  and   its  Ap- 
plication to  the   Precise  Testing  of  Hydro-Electric  Generators". 
Trans.  A.S.C.2.,  Vol.   LXXX,    1916.) 

Gurley,  V,r.  &  L.  E. : 

"Manual  of  Gurley  Hydraulic  Engineering  Instruments". 

Hele  Shaw,  H.  S. : 

"Experiments  on  the  Nature  of  the  Surface  Resistance  in  Pipes 
and  on  Ships".   (Trans.  Inst .  Naval  Arch.,  1897.) 
"investigation  of  Stream  Line  Motion  Under  Certain  Experimen- 
tal Conditions".   (Trans.  Inst.  Naval  Arch.,  1898.) 
"Stream  Line  Flow  of  a  Viscous  Fluid".   (Report  of  British 
Assn.,  1898.) 

"The  Distribution  of  Pressure  Due  to  Flow  Round  Submerged  Sur- 
faces".  (Trans.  Inst.  Naval  Arch.,  1900.) 
"The  Motion  of  a  Perfect  Fluid"1. 

Hoff,  E.  J.: 

"Current  Meter  Studies". 

Hoyt,  W.  G.: 

"The  Effects  of  Ice  on  Stream  Flow".   ('iTater  Supply  Paper,  No. 
337,  U.  S.  Geological  Survey.) 

Hoyt  and  Grover: 

"River  Discharge". 

Hydraulic  Labratory,  Colorado  Experiment  Station,  Ft.  Collins,  Colo. 
Tables,  Tests,  Rating  Data,  etc. 


Not  available. 


86 


Lyon,  G.  J.: 

"Equipment  for  Current  Meter  Gaging  Stations".   (Water  Supply 
Paper,  No.  371,  U.  S.  Geological  Survey.) 

Murphy,  E.  C.: 

"Accuracy  of  Stream  Measurements".   (.Tater  Supply  Paper,  No. 
95,  D.  S.  Geological  Survey.) 

"Current  Meter  and  "reir  Discharge  Comparison".   (Trans. 
A.S.C.E.,  Vol.  XVI,  1887.) 

Noble,  T.  A.: 

"Current  Meters".   (Trans.  A.S.C.E.,  Vol.  XLI-2,  1899.) 

Rensselaer  Polytechnic  Institute,  Troy,  N.  Y. : 
Thesis  on  Current  Keters  . 

Sandstrom,  J.  ".. .  : 

"Hydrometric  Experiments".   (Stockholm,  1912.)   (Manuscript 
in  the  Office  of  Irrigation  Investigations,  Berkeley,  Calif.) 

Schmidt,  1.1.  : 

"Untersuchungen  uber  die  Umlaufbewegung  hydrometrischer  Flugel". 
(ilitte  i  lunge  n  uber  Forschungsarbeiten  auf  dem  Gebiete  des  Inge- 
nieurwesens,  1903.) 

Scobey,  F.  C. : 

"Behavior  of  Cup  Current  Meters  Under  Conditions  Not  Covered 
by  Standard  Ratings",   (journal  of  Agricultural  Research,  Vol. 
II,  No.  2,  1914.) 

Stearns,   F.   P.: 

"On  the  Current  Meter  Together  With  a  Reason  IThy  the  Maximum 
Velocity  of  Water  Flowing  in  Open  Channels  is  Below  the  Sur- 
face". (Trans.  A.S.C.E.,  Vol.  XII,  1883.) 

Unwin,  "f.  C.: 

"Hydraulics".   (Encyclopaedia  Britannica.) 
"Hydromechanics".   (Enclyclopaedia  Britannica.) 

Fortier  &  Hoff: 

"Defects  in  Current  Meters  and  a  New  Design  .   (Engineering 
News-Record,  Vol.  85,  No.  20,  1920.) 


1 
Wot  available. 


87 


I8DEX. 

Reference  to  pages. 

Contour  curves,  7. 
Current  meters, 

demands  on  for  irrigation  work,  6,  54. 
fundamentals,  6. 
historical,  1. 
horizontal  shaft,  31'. 

air  meter  type,  31,  32. 

ideal  curve,  31. 

rating  curve,  30. 
Hoff,  5,  16. 

advantages,  61. 

disadvantages,  82. 

equation,  71. 

rating  curve,  34,  35,  55,  68. 

surface  curve,  37,  38. 
ideal  measurements,  requirements,  52. 

possibilities  of  realization,  53. 
method  of  measuring  stream  flow,  3. 
only  scientifically  designed,  4. 
Price,  2,  20. 

as  horizontal  shaft,  50. 

rating  curve,  18. 

surface  curve,  29. 
vertical  shaft,  17. 

advantages,  58. 

disadvantages,  59. 

ideal  curve,  20. 

rating  curve,  16,  28. 

without  rigid  support,  29. 

Eddy  currents,  definition,  3. 
effects,  9. 
reactive  force,  11. 

Higher  velocity  curve,  definition,  20. 
Interference,  see  Resistance. 
Obstacles,  6,  42. 

Parallel  filaments,  4,  7. 
Propeller,  62. 

definition,  1. 

mass,  54. 

Rating   curves,   factors   affecting,   see   Interference. 
Resistance,   Hoff  theory,   17. 

explanation,   17. 

proof,   50. 


88 


Rod  in  strean,  13. 

Starting  velocity  curve,  definition,  20. 
Stream  filaments,  energy,  10. 
parallel,  4,  7. 

Turbine,  definition,  1. 

explanation  of  rotation,  17. 

Vacuous  spaces,  13. 
Vertical  velocity  curves,  7. 
Viscosity,  effect,  7. 


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